`(cos4A + cos2A)/(sin4A - sin2A)` =`(1)/(tan A)`  Prove the double angle identity

1 Answer | Add Yours

justaguide's profile pic

Posted on

The identity `(cos 4A + cos 2A)/(sin 4A - sin 2A) = 1/tan A` has to be proved.

`(cos 4A + cos 2A)/(sin 4A - sin 2A)`

= `(2*cos^2 2A + cos 2A - 1)/(2*sin 2A*cos 2A - sin 2A)`

= `(2*cos^2 2A + 2cos 2A - cos 2A - 1)/(2*sin 2A*cos 2A - sin 2A)`

= `(2*cos 2A(cos 2A + 1) - 1(cos 2A + 1))/(2*sin 2A*cos 2A - sin 2A)`

= `((2*cos 2A-1)(cos 2A + 1))/(sin 2A*(2*cos 2A - 1))`

= `(cos 2A + 1)/(sin 2A)`

= `(2*cos^2A -1 + 1)/(2*sin A*cos A)`

= `(2*cos^2A)/(2*sin A*cos A)`

= `(cos A)/(sin A)`

= `1/tan A`

This proves that `(cos 4A + cos 2A)/(sin 4A - sin 2A) = 1/tan A`

We’ve answered 319,784 questions. We can answer yours, too.

Ask a question