Can anyone help me verify this equation is an identity please? : 2(sinx-sinx³)/cosx=sin2x

Question

4252 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-07T01:28:22

As explained.

#(2(sin x - sin^3x) ) / cos x = sin 2x#

enter image source here
#sin 2x = 2 sin x cos x# using double angle formula.

#(2sin x(1 - sin^2x)) / cos x = 2 sin x cos x#
enter image source here

#1 - sin^2x = cos^2 x# using the identity.

#(cancel (2 sin x) cos^2x ) / cos x = cancel (2 sin x) cos x#

#cancel (cos^2x ) / cancel (cos ^2x) = 1#

Q E D