Question

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.

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

so LHS = 1 + tan^2 x

Answer 6

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?

Answer 7

right

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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 :)

Answer 18

yw