Re: TRIGONOMETRY IDENTITIES

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Posted by Louis Feng on October 22, 1998 at 21:19:30:

In Reply to: Re: TRIGONOMETRY IDENTITIES posted by ROBYN REAMS on October 19, 1998 at 14:13:25:

Hi Robyn,

We can use some fundamental identities to prove this problem.

First of all, we want to reduce the differences between the two sides. To reduce the difference of operations, we convert left side to multiplication.

L= (1+tan^2A)/tanA

By the fundamental identities, we know that 1+tan^2A equals to sec^2A, which is what we want.

L=sec^2A/tanA

We can write it as:
L= secA*secA*(1/tanA)
=secA*secA*cotA

We already got secA, which we want to keep it. Then we know the rest, which is secA*cotA should equals to cscA. To do this we need convert secA and cotA to sinA and cosA, so that we can cancel some terms. We have:

L=secA*(1/cosA)*(cosA/sinA)
=secA*(1/sinA)
=secA cscA
=R

I encourage you to look thru our web pages, which will give you many tips and strategies on those kind of problems. You will find problems are becoming easier and easier to solve. If you have any quesitons or problems feel free to post them here. If we can't solve them, other people might be able to help you out. Good luck.

Best regards,

Louis

: : : 1/TANA + TANA = SECA CSCA

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Comments: : Hi Robyn, : We can use some fundamental identities to prove this problem. : First of all, we want to reduce the differences between the two sides. To reduce the difference of operations, we convert left side to multiplication. : L= (1+tan^2A)/tanA : By the <a href="http://hyperion.advanced.org/17119/je/memorize/basic.html">fundamental identities</a>, we know that 1+tan^2A equals to sec^2A, which is what we want. : L=sec^2A/tanA : We can write it as: : L= secA*secA*(1/tanA) : =secA*secA*cotA : We already got secA, which we want to keep it. Then we know the rest, which is secA*cotA should equals to cscA. To do this we need convert secA and cotA to sinA and cosA, so that we can cancel some terms. We have: : L=secA*(1/cosA)*(cosA/sinA) : =secA*(1/sinA) : =secA cscA : =R : I encourage you to look thru our web pages, which will give you many tips and strategies on those kind of problems. You will find problems are becoming easier and easier to solve. If you have any quesitons or problems feel free to post them here. If we can't solve them, other people might be able to help you out. Good luck. : Best regards, : Louis : : : : 1/TANA + TANA = SECA CSCA

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