Question

Establish the Identity:

Answer 1

I'd probably start on the left, multiply the numerator and denominator by (sinx + cosx).

Then change the cos^2 x which will be in the denominator into 1-sin^2 x.

Then i think you'll have the right hand side... i think i just solved it in my head :D

Answer 2

\[\large \frac{ (\sin x + \cos x) (\sin x + \cos x) }{(\sin x - \cos x) (\sin x + \cos x) } = \]
\[\large \frac{ \sin^2 x + \cos^2 x + 2 \sin x \cos x }{\sin^2 x - \cos^2 x} =\] now replace the sin^2x+cos^2x with 1
\[\large \frac{ 1 + 2 \sin x \cos x }{\sin^2 x - (1- \sin ^2 x)} =\]

Answer 3

ok I follow the numerator to the end, but the denominator in your last step to 2sin^2x-1 I am not following.

Answer 4

i see sin^2 - sin^2 -1 which =-1?

Answer 5

oh wait I have to factor the negative sign?

Answer 6

I see it now thank you.

Answer 7

There's no set way to solve identities. Sometimes you just have to do crap and see what happens. Let it ride!

Answer 8

I think I will do better once the basic identities are second nature. I just don't "see" some of the correlations that are obvious to people who have used trig for some time.

Answer 9

Yep, it comes with practice. I remember hating proving identities in high school.. now i kinda like it.

Answer 10

I went from pre algebra in 1979 to precalc this year, no school in between. Life experience allowed me to do well on the placement test... whish I didn't skip algebra 2 though.