Question

prove that cos secant theta minus sin theta into secant theta minus cos theta equal to one by tan theta + cot theta​

Answer 1

Step-by-step explanation:

To prove,

(cosec θ - sin θ)(sec θ - cos θ)(tan θ + cot θ)=1

Proof:

LHS =(1/sin θ - sin θ)(1/cos θ - cos θ)(tan θ+1/tan θ)

        =(1-sin²θ)/sinθ (1-cos²θ)/cosθ(1+tan²θ)/tanθ

        =(cos²θ)/sinθ (sin²θ)/cosθ sec²θ/tanθ

        =cos θ sin θ (1/cos²θ)/(sinθ/cosθ)

        =cos θ sin θ(1/cos²θ)(cosθ/sinθ)

        =cos θ sin θ (cos θ/sin θ cos²θ)

        =cos θ sin θ (1/sin θ cos θ)

        =cos θ sin θ/sin θ cos θ

        =1=RHS

           ∴ Hence proved