Question

verify the identity:

(1-2 sin^2 θ)/(sin θ cos θ)=cot θ-tan θ

Answer 1

cotx-tanx= cosx/sinx - sinx/cosx.

Which becomes cos^2x-sin^2x/sinxcosx.

cos^2x-sin^2x=1-2sin^2x.

So the right side now looks like 1-2sin^2x/sinxcosx. And you're done

Answer 2

let x=theta

Answer 3

so 1-2sin^2x/sinxcosx is the identity?

Answer 4

Yep

Answer 5

\[\cot \Theta = \frac{ \cos \Theta }{ \sin \Theta }\]
\[\tan \Theta = \frac{ \sin \Theta }{ \cos \Theta }\]

\[\frac{ \cos ^{2}\Theta - \sin ^{2} \Theta }{ \cos \Theta \sin \Theta }\]

alright so far?

Answer 6

Does that make sense?

Answer 7

yeah thanks!

Answer 8

Good! :) You're welcome

Answer 9

\[\cos ^{2} \Theta = 1- \sin ^{2} \Theta\] Insert that into the cos pat and wala\[\frac{ 1 - \sin ^{2} \Theta }{ \cos \Theta \sin \Theta}\]