1 + sec^2 x sin^2 x = sec^2 x
Verify this trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

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- cwrw238

LHS: use sec^2 x = 1 /cos^2 x

- anonymous

Thanks for answering but I still don't get it. What do you mean?

- cwrw238

LHS = 1 + sin^2 x
-------
cos^2 x

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- cwrw238

and sin^2 x
------- = tan^2 x
cos^2 x

- cwrw238

so LHS = 1 + tan^2 x

- anonymous

ok... so let me see if this will help you help me understand this better.
I know that I'm supposed to do something with the left side of the equation to make it sec^2x. correct?

- cwrw238

right

- anonymous

I just don't see how the cos^2x in the denomenator fits in. I'm sorry I truly suck at this :(

- cwrw238

yes these can be tricky - you must have a good knowledge of the trig identities
sometimes you just try different ones to see if there are any connections
- i was aiming for 1 + tan^2 x because i knew that sec^2 x = 1 + tan^2 x

- cwrw238

i introduced the cos^2x because sin^2 x/cos^2 x = tan^2 x and sec^2 x = 1/cos^2 x

- anonymous

OK so how would I put that together to get the answer

- cwrw238

if you google trigonometrical identities you'll a list of them

- anonymous

starting from the original equation how do I use what you gave me.

- cwrw238

well we got LHS = 1 + tan^2 x and this equals RHS sec^2 x

- anonymous

yes but then again so does 1+ sec^2x sin^2x. I need to transform (1+sec^2xsin^2x) and make it read sec^2x

- cwrw238

LHS = 1+sec^2xsin^2x)
= 1 + sin^2 x
------ (because sec^2 x = 1 / cos^2 x)
cos^2 x
= 1 + tan^2x
= sec^2 x ( because sec^2x = 1 + tan^2 x is a standard identity)
= RHS

- anonymous

Ohhhhh got it wow! OK. Thank you so much. You see I suck so bad that even when you are plainly explaining it to me I still dont get it. But now I do. Again thank you for helping me :)

- cwrw238

yw

- anonymous

|dw:1354034596449:dw|

- anonymous

above the last equal sign.... what does it say? 1/??

- anonymous

oh wait is it 1/cos^2x ?

- anonymous

yeah sister

- anonymous

awesome.... ok thanks but why is yours different than the other one? is it wrong or is this just another way to do it

- cwrw238

no - they are both acceptable - just another way to do it

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