Question

Establish this identity

Answer 1

see explanation

Explanation:

Using the identities

tan x =
`(sinx)/(cosx)` , sin²x = 1 - cos²x

sin2x = 2sinxcosx

Consider left side

cosθ × sin2θ

=
`(sin0)/(cos0)` × 2sinθcosθ ( cancel cosθ )

= 2sin²θ

= 2(1 - cos²θ)

= 2 - 2cos²θ

= right side , then established