Question

prove the identity: sin theta + (cos theta/tan theta)=1/(cos theta tan theta)

Answer 1

sinθ + (cosθ/tanθ)
= (sinθ * tanθ/tanθ) + (cosθ/tanθ)
= (sinθ * tanθ + cosθ)/tanθ
= (sinθ * sinθ/cosθ + cosθ)/tanθ
= (sin^2 θ/cosθ + cosθ * cosθ/cosθ)/tanθ
= (sin^2 θ/cosθ + cos^2 θ/cosθ)/tanθ
= ( [sin^2 θ+cos^2 θ]/cosθ)/tanθ )
= (1/cosθ)/tanθ
= 1/(cosθ*tanθ)

LHS = RHS