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Find the exact value of the expression: Do not use a calculator: cot 60` sin 4592-V OA 22 - 13 0 B. 2213 - 312 0c:212 - 313 0 D....

Question

Find the exact value of the expression: Do not use a calculator: cot 60` sin 4592-V OA 22 - 13 0 B. 2213 - 312 0c:212 - 313 0 D.

Find the exact value of the expression: Do not use a calculator: cot 60` sin 459 2-V OA 2 2 - 13 0 B. 2 213 - 312 0c: 212 - 313 0 D.



Answers

Find the exact value of the expression whenever it is defined. (a) $\sin \left[\frac{1}{2} \cos ^{-1}\left(-\frac{3}{5}\right)\right]$ (b) $\cos \left(\frac{1}{2} \sin ^{-1} \frac{12}{13}\right)$ (c) $\tan \left(\frac{1}{2} \tan ^{-1} \frac{40}{9}\right)$

In this question we have to solve exact values of the expression that are given to us. The first expression is sign up. Ah well of course in worse -3 x five. Okay that's all this expression first of all we should know that if there is minus in the post in worse then it changes into by minus course universe sex. And if there is Sign off by by 2- Theatre then it provides you cost data. Okay so we are using here both these formulas. First of all I write it as a sign up for by minus causing worth three by five. Okay now I make half then. Bye Bye. To minus or half of course anniversary by five. The next changes into Because of half of cause anniversary by five by this formula. Okay now let us assume that This course in verse three x 5 years theatre Then it provides the value of course data, that is three x 5. Okay so I use it here regard it from course theater but I do because I had taken this as theater. Now you can say that formula for prostate of my duties. The root of one plus force him to veto. And I put here the value of pasta that is three x 5. And after putting this value these changes into paid by five x 2. And after cancellation we get here to buy Road five. Okay this is the answer of the first question here. Now in the second part we have to find the value of awesome half of signing words Well by 13. Okay So first of all let I assume this signing was 12 by 13 years theatre. Then this provides the value of science theater and then I get the value of pass it up from here. 13 is hyper tennis which remains as it is And perpendicular is 12. The calculated base that comes out to be five. Okay now we put this Substitution that these changes in the cost to buy two. Now it's formulas again due to one was posted to buy two and we have to put the value of pasta that we had calculated years five x 13 if I didn't like to okay with all this explosion then it changes into nine by I can say they're 13 and it's Protest three by a vote of 13. Okay, this is the and throw the second question here. Now the third question says that we have to so the exploration that is then No. Uh huh. 10 universe 40 x nine. Okay. To solve it, let I take my 10 inwards 40 x nine it was to theater. This provides the value of 10th that is 40 x nine. Now I calculate cost it up from here. So the value of post theater should be based upon hard retainers basis. Nine and high Putin has comes out to be 41. Now we substitute this in the question so it changes into 10 of data by two because we had taken this as data now to find the 10 ft away to formula is the root of one minus course guitar one. When plus course data we put the value of course it. To hear value. Of course it was nine by 41 so one plus nine by 41. In the liberated after calculation you get 32 x 41 and in the denominator you get here 50 x 41 after translation and doing the square root Will we get four x 5? Okay this is the answer of the last part here. Thank you.

In this question we have to fall three eggs actual equations. First of them is sign up, go down any worse. five x 12. Okay. So to solve it, you know the formula of 2, 10 And we're sex in the in terms of signing the words Nowadays towards divided by one plus access. Well so I'm going to apply this formula here. So we get here so I know sign in words to works access by by it. Well Upon one class access square that is five x 12 square. Okay. Now we can say that sign and signing what's cancel out And after solving this whole time you get here recently won 20x169. Okay. This is the answer of they first fired here. Now in the second part we can say that I have to found. Well of course of to cause in worse nine x 41. Okay. The full weight that is a formula of Cocos universe. The formula says that because you know what sex is. It was too Course and was to work Square -1. So I applied this formula so we get clear corso course universe. To access where Mean Square of nine x 14 -1. Okay your cause and causing what's cancel out. And after that we have to solve this expiration and we get here finally minus off 1519 divided by 1681. Okay this is the answer here for the second question and indeed third part We have to solve the exact value expression of 10 of to sign in words -15 x 17. The first of all you're gonna see your debt. There is a formula that says that signing hours of minus sets. Music was to minus outside universe. Sex And 10 of- Data is also it was 2- of Santa. So we applied body formulas here so we get 10 of minus tools sign in words 15 by 17. Since we take minus outside outside universe. And after that we can take this minus outside of Our 10 also. So you get -10. You'll sign in the worst. 15 x 17. Okay, now, first of all, I am going to convert this Signing words into 10 universe. So while you can warden of this sign universe into town universe, I am making here a right angle triangles. Okay, and in this right angle triangle, I am going to mark your angle and new york Sign universes, horatio of perpendicular that is 15 and hybrid owners that is 17. And we find the base. So our base comes out to be it. Okay, Now I use this year. So this is converted into 10 universe. We should have to divide the perpendicular. That is 15 and based 18, 8. Okay. How I apply the formula of Sudan universe. The formula to 10 universities Danny was To access were means to 32 x. Okay upon 1- Access. Word means 15 x eight police class. Now you can look here that your 10 and 10 universe chance laws and after that we have to solve this exploration and we get minus c minus off- of 2 40, lie 1 61. Okay, and this cancels your minus. So we get finally to 45-161. This is the point of answer of the third question here. Okay, thank you.

Way had you compute about a side after four by three and and the anger underfoot by the three minutes in the cotton tree and in the couldn't read assigning co Judah minors off square root of a tree and to But we we have to fight the second after 11 pi out of sex and the second we know Ingrid ICO to one off course, I'm that 11 pi on top six and ankle even by other six. We have to go sign and we'll include you. No, screw the tree and a Jew and therefore get it too. I'm the squinted three in the pussy. We need to fight the Goa tension off Germans by out of three because potentially is the old function never would have a monusco tension under pie under a tree on the angle of the point of three Kodansha Inco Junior. One hours with three

This question we have to fall three tournament trigger expressions and we are to simplify all of them. First one is you know, to 10 inwards five bite well, okay, so the formula to solve it is to turn inward sex can be organized in the form of signing words that is two weeks upon one plus taxes square. So I apply this formula so I got signed up sign animals to work, means to and to fight by 12 upon one plus access requirements five by 12 were okay now with all this. So after following a tiger, sign up, signing what? Saw 1 20 by 1 69 and after the cancellation of signed by signing, what's I get? 1 25 1 69. Okay, this is the answer for the first question. Now in the second part, we have to solve here. That is it was too, I can say that course. So to cause in was nine by 41. Okay. To solve it, we have the formula of two cores in what sex that is, it was too coarse in was to access square minus one. So I oblige this formula years. So I get here because of course in what's to access square means two into nine by 41 square minus one. Okay. And after solving this regard here call so causing were so I can say that here minus of one 519 divided by 1681 Okay. And after cancellation of course by course and once we get minus 1519 divided by 1681 This is the answer for the second part. Okay And now in the third part we have to Seoul the given question that if it was too and or to sign in words okay minus eight by 17. First of all I'm applying the property that says that signing worth minus X can be written minus sign in ward six and 10 of minus state. I can give it an a minus of 10 data. So I apply both these properties of material and in the worst economic questions. So I got here first of all, 10 of minus two signing works. Eight by 17. Okay, now from 10 also this minus votes Outsides of minus of 10 of to signing the worst the midwife, 17. Okay, now we are going to convert this sign inwards in the form of 10 and work. And if you convert it in the form of 10 inwards, then you can see that in this right angle triangle you have perpendicular and high potentates 17. If you find the base by by the water then it comes out to be 15. So I put here perpendicular upon days that is eight by 15. Okay, now we are going to apply the formula to 10 and we're sex and the formula says that you have to right here, tienen was two X upon when minus taxes would so I apply this year so I should get here minus stand now. Then in the words of the works means to into eight by 15 upon one minus success square means eight by 15 whole squad. Okay, now we have sold this and after solving this we get the value that if it was too, I can say that to 40 by 1 61. Okay now we are going to cancel 10 by 10 in worse. So we get here finally, the value that is it was two minus 2 40 by 1 61. Okay, this is the answer for the card question here. Thank you.


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