Question

Steps on how to establish this identity:
(secθ-cosθ)/(secθ+cosθ) = sin²θ/(1+cos²θ)

Answer 1

\[\frac{ 1-\cosθ }{ 1+ \cosθ } = \frac{ \sin²θ }{ 1+\cos²θ }\]
I'm at this step. Is it okay to square the left hand side to make it equal to the right even though I'm not squaring both sides?

Answer 2

Hey, you multiply the whole thing you should get
\[\frac{1-\cos^2x}{1+\cos^2x}\]

Answer 3

by cosx*

Answer 4

\[\frac{secx-cosx}{secx+cosx} \\ \\ \huge \frac{\frac{1}{cosx}-cosx}{\frac{1}{cosx}+cosx} \times \frac{cosx}{cosx} \\ \\ \huge \frac{1-\cos^2x}{1+\cos^2x}\]

Answer 5

Then use identity \(sin^2x=1-cos^2x\)

Answer 6

Got it. You made it look really easy! Thanks! :)

Answer 7

welcome :)