Question

prove that cos theta - sin theta / cos theta + sin theta = sec 2 theta - tan2 theta

Answer 1

Answer:

(Cosθ - Sinθ)/(Cosθ + Sinθ) = Sec2θ - Tan2θ

Step-by-step explanation:

Prove that cos theta - sin theta / cos theta + sin theta = sec 2 theta - tan2 theta

(Cosθ - Sinθ)/(Cosθ + Sinθ) = Sec2θ - Tan2θ

LHS

= (Cosθ - Sinθ)/(Cosθ + Sinθ)

= (Cosθ - Sinθ)/(Cosθ + Sinθ)  * (Cosθ - Sinθ)/(Cosθ - Sinθ)

= (Cos²θ + Sin²θ  - 2CosθSinθ) /(Cos²θ - Sin²θ)

= ( 1  - 2CosθSinθ)/(Cos²θ - Sin²θ)

= (1 - Sin2θ)/(cos2θ)

= 1/cos2θ  - Sin2θ/cos2θ

= Sec2θ - Tan2θ

= RHS

QED

(Cosθ - Sinθ)/(Cosθ + Sinθ) = Sec2θ - Tan2θ

Answer 2

Step-by-step explanation:

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