prove: sinθ cosθ = (cosθ - cos^3θ)/sinθ

Question

i need all steps.

Answer 1

Remember the formulae

Sin^2Ѳ+Cos^2Ѳ = 1

CotѲ = CosѲ/SinѲ

Right handside identity

= (CosѲ-Cos^3Ѳ)/SinѲ

= CosѲ/SinѲ - Cos^3Ѳ/SinѲ

= CosѲ/SinѲ - Cos^2ѲCosѲ/SinѲ

= CotѲ - Cos^2ѲCotѲ

= CotѲ(1-Cos^2Ѳ)

= CotѲSin^2Ѳ

= (CosѲ/SinѲ)Sin^2Ѳ

= CosѲSinѲ

= Left hand side identity.