2(sinx-sin^3 x)/cosx = sin2x ?

Question

verify the identity

Answer 1

Greetings! Lets solve this shall we ?

So, we must use trig identities to confirm the identity on the right side of the equal sign in this case. Then,

2(sinx - sin³x) / cosx = sin2x.............Factor out a sinx such that

2sinx(1 - sin²x) / cosx = sin2x..............Replace the identity cos²x = 1 - sin²x such that

2sinx(cos²x) / cosx = sin2x.................Cancel one cosx to obtain

2sinxcosx = sin2x.............Identity confirmed!

I hope this helped!