CKaterinaR 3 years ago 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.

1. cwrw238

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

2. CKaterinaR

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

3. cwrw238

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

4. cwrw238

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

5. cwrw238

so LHS = 1 + tan^2 x

6. CKaterinaR

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?

7. cwrw238

right

8. CKaterinaR

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

9. 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

10. cwrw238

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

11. CKaterinaR

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

12. cwrw238

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

13. CKaterinaR

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

14. cwrw238

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

15. CKaterinaR

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

16. 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

17. CKaterinaR

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 :)

18. cwrw238

yw

19. jishan

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20. CKaterinaR

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

21. CKaterinaR

oh wait is it 1/cos^2x ?

22. jishan

yeah sister

23. CKaterinaR

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

24. cwrw238

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