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Find the exact value of each of the following under the given conditionscos (a + B)b. sin (a + 8)tan (a + B)tan & = 4,I<a <-and cos p =2 < B < 21cos...

Question

Find the exact value of each of the following under the given conditionscos (a + B)b. sin (a + 8)tan (a + B)tan & = 4,I<a <-and cos p =2 < B < 21cos (a + B)=l (Type an exact answer using radicals as needed_ Simplify your answer: Rationalize all denominators_ Use integers or fractions for any numbers in the expression:)

Find the exact value of each of the following under the given conditions cos (a + B) b. sin (a + 8) tan (a + B) tan & = 4,I<a <- and cos p = 2 < B < 21 cos (a + B)=l (Type an exact answer using radicals as needed_ Simplify your answer: Rationalize all denominators_ Use integers or fractions for any numbers in the expression:)



Answers

find the exact value of each expression. Write the answer as a single fraction. Do not use a calculator. $$ \sin \frac{3 \pi}{2} \tan \left(-\frac{8 \pi}{3}\right)+\cos \left(-\frac{5 \pi}{6}\right) $$

So we want to find the exact value of our following expression. Let's recall that if you have co sign of a Times Co sign of B and we add that with sign of a 10 sign of B, we can rewrite this as co sign of a minus. Being here, we're going to have sign or actually, that's been to post on of seven pi over eight, minus six phonetics by, um, that's going to be pi over eight. So this gives us that we have co sign of six high over eights from what is that? Well, six by over eight. We can rewrite this as two times three pie over two times for council of that, too. So here we have three pi over four. Okay, so this is co sign of three pie over four. We know that this is equal to the negative square root of 2/2

So be a concern of 12. Thank you, Sino 78 plus cause an upset You times a sign of 12 degree. Never call that casino 12 degrees is he go to sign of 90 minutes. 12. He's I usually have a sign of 78 degrees here, and on the other hand, we have comb side of suddenly degrees. Times signed told of these, which is you got to come so early. 19 minus two degrees. It's a sign of 1,000,000 minus 12 is a sign of 78. So your silence and your time sort of 78 degrees was consuming. So you, to these times, come soon. Oh, so you degrees still find this mystery squared of 78 degrees was coasting screen of 78 degrees. You'll recall that sine squared exposed goes into it, says you go to one. So instead of accepting of 70 degrees, but either way, this is just to go to one

In this question, we have to find the value off course off 12 degrees multiplied would sign off 78 degrees plus course off 78 degrees multiplied with sign off 12 degrees. Now, using the compliment laws we can write goes off to real degrees multiplied with sign off. 70 degrees can be written as course or 90 miners. 78 degrees plus course off 70 degrees can be returners, Sino 90 degrees minus 78 degrees multiplied with sign off 12 degrees. No, we can light it as course off 12 degrees multiplied with course off 90 degrees minus 70 degrees. Gives us close off the well degrees plus sign off. Well, degrees multiplied with sign off 12 degrees. Solving it we get course square, 12 degrees plus sine squared well degrees. Using the identity called Square Tita plus sine squared three take was one we get the answer is one here

Hit for this problem. They want us to compute the tension of the art engine of and they want us to compute on other thing, the It's the sine inverse of the sign. Ah, seven pi over three. Okay, now, this question here is pretty clear. Well, the our attention of 10 is going to give us a unique angle. That unique angle correspond exactly back to 10 okay, within its range. So we just have that these two in verses cancel out nicely on the stuntman and give us 10. However, this is a little more intricate because sign is to find for its stunning and range on a unique and through. So first, let's take the sign of seven by over there, uh, seven pi over three is let's see more than two pi, and in fact, it's to pipe plus high over the ring. So if you look at the unit circle, we're going to end up with 1/3 of a pie here. However, when we take, the inverse were restricted. Teoh this domain over here. But where is it the same for this value? It iss this right? So we're gonna end up with negative pi over three in this case. Yeah,


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