Question

Prove
that
sinΘ-2sin³Θ/2cos³Θ-cosΘ=tanΘ

...theta=Θ​

Answer 1

Answer:

LHS = RHS

Step-by-step explanation:

sinΦ(1-2sin²Φ)/cosΦ(2cos²-1) = tanΦ

=>sinΦ(cos²Φ-sin²Φ)/-cos(sin²Φ-cos²Φ)=tanΦ

=>sinΦ(cosΦ-sinΦ)(cosΦ+sinΦ)/

-cos(sinΦ-cosΦ)(cosΦ+sinΦ) = tanΦ

=>sinΦ(cosΦ-sinΦ)/cosΦ(cosΦ-sinΦ) = tanΦ

=>sinΦ/cosΦ = tanΦ

=> tanΦ = tanΦ

Hence, LHS = RHS Proved.

theta = Φ

Answer 2

sin²θcosec(90°-θ) - cot²(90°-θ)cosθ = sin²θ/cosθ - tan²θ cosθ = sin²θ/cosθ - sin²θ/cosθ cos²θ

= sin²θ/cosθ - sin²θ/cosθ = 0

Please follow me if you found this helpful