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Establish the identity: cos 0 < tan 0 = sin Write the left side in terms of sine and cosinecoSWrite the result from the previous step as a single fraction_(Do no...

Question

Establish the identity: cos 0 < tan 0 = sin Write the left side in terms of sine and cosinecoSWrite the result from the previous step as a single fraction_(Do not simplify:)The fraction from the previous step then simplifies to sin 0 using what?OA Cancellation Property 0 B. Even-Odd Identity 0 C. Pythagorean Identity 0D: Reciprocal Identity Quotient Identity

Establish the identity: cos 0 < tan 0 = sin Write the left side in terms of sine and cosine coS Write the result from the previous step as a single fraction_ (Do not simplify:) The fraction from the previous step then simplifies to sin 0 using what? OA Cancellation Property 0 B. Even-Odd Identity 0 C. Pythagorean Identity 0D: Reciprocal Identity Quotient Identity



Answers

Verify the identity. $$\begin{aligned} &a \sin B \theta+b \cos B \theta=\sqrt{a^{2}+b^{2}} \cos (B \theta-C), \text { where }\\ &C=\arctan (a / b) \text { and } b>0. \end{aligned}$$

We need to prove that scientific data upon one minus coast teeter is equal to B one plus cost data Upon scientific, we need to produce the result in two ways. Now, by first away, we have left and say, Is he going to be scientific? Over one minus costing? Now, by nationalizing that nominated, this will become scientists over one minus cost data multiplied with one plus co state are divided by one plus Costa Now by simply saying it will become scientists, My replied with one plus course data divided by one minus cost. My people, I e. One plus coast Now, by using the result that a minus bi my replied with a plus B is equal to be a diploma to Finance Minister Barbara to this will become scientists multiplied with one plus course. Take that upon one minus coarse scale. Now we have This will become is equal to be scientifically by deploying one place Coast data divided by sign skilled enough now because science Concetta Klesko's capita is equal to be. But now I can sing sine theta sine theta. This will become one plus coast data divided by sine theta, which is equal to be the right inside. Now, secondly, we need to blow that scientists over one minus casita. Now, by multiplying and divide the given with science data we have this will become is equal to be science. Concetta divided by sine theta my replied with one minus coast data. Now we can delight it as one minus core skills hitter divided by sine theta. My replied with one minus course it now, but using the formula that status to power to minus videos to power two is equal to be a minus bi my plan with a bless me this will become one plus coast data my deployed with one minus coast data divided by sine theta by people. I read one minus course data canceling when miles course hitter with one minus supposed this will become is equal to be one less course data divided by sine theta. So it is a little bit right in sight. So this is the proof of the given results by using two ways. So this is our answer

Proceeding from charities which is equal. Do under fruit off case car place be ascribed, multiplied by a sign off. Beat it plus C. We're Sesay. Call Toe Park 10. Be divided by a no clearly sees nothing but equal toe Act on. Be divided by a and that is equal to our sign. Be divided by underdog. Yes, God Bless via Square, which is equal toe arc course. Hey, divided by under Newt off a squared plus B squared further from artists, we can proceed as a squared plus B squared under route sign Be teeter cough C plus course Beat eater Science E and we can write underwater off a strapless B squared sine beat eater and costs he will be equal to I think what 80 Wedderburn, Don't go face complice beer square. Bless course be teeter multiplied will be divided. Vanderhof, Fiesta plus B s quest. This can be simply fired as he is saying Beat eater, Bless because will be ticker and that is it will do Elytis

Bonus problem. We're going to use our product to some and some to product formulas in order to prove this identity. So we're going to confer to the left side into the right side. It's generally easier to start with the more complicated looking type and simplify it into the simpler side. So there are two product to some identities that we're going to use here. The 1st 1 is that sign a time sign be he calls 1/2 times Co sign of a minus bi minus co sign of a plus B, and the 2nd 1 that will be using is sign of a Times Co side be. It was 1/2 time sign of eight must be plus sign of a minus bi, and the reason we're going to be using these is that they look a lot like the numerator and denominator of our left hand side expression and dropped their identical except for there is a 1/2 in front of each. So, in order to get them identical so that we can substitute will multiply both sides of these identities right to, so we'll get to side. I signed me into the White House and to sign a coast speaking and get rid of. So now we have this identical so we can substitute in these expressions. So our numerator So we'll take our left hand side. The numerator will become to sign a signed B and the denominator. It will substitute in two side. A cause I'd be. And then we can simplify this because the twos Wilkins a lot and the sign is will cancel out. So we have signed B over co sign be because they have the same infant. We You know that sign of our coastline is tangent. This will be equal to attach it to be attention of B is our right hand side. So we've converted the left hand side into the right hand side, which is exactly what we wanted to do. So that means that this identity is now verified.

This is our fallen number 64 in which Ah, we need to do that. NTT. Okay, well into very father entity. By transforming left hand side into right and side left himself. So our question is signed, Tita place cause theta because he take all toe one place, 10 theta. So we have our left hand side scientists plus cost theater by cause theater Now separating it out we'll be getting science theater by cost theta class cause theater by cost theater Now these two will get canceled out And according to the quotient Identity Science Theater Because theater will be called to 10 theater. So if right, this one here. So it will be one place 10 theater, which is our right inside. Thank you so much.


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