Question

Prove that (1 + cot θ - cosec θ)(1 + tan θ + sec θ) = 2

Answer 1

HELLO DEAR,



(1 + cotθ - cosecθ)(1 + tanθ + secθ)

=> (1 + cosθ/sinθ - 1/sinθ)(1 + sinθ/cosθ + 1/cosθ)

=> {(sinθ + cosθ - 1)/sinθ} {(cosθ + sinθ + 1)/cosθ}

=> {(sinθ + cosθ)² - 1}/sinθcosθ

=> {(sin²θ + cos²θ) + 2sinθcosθ - 1}/{sinθcosθ}

=> {1 + 2sinθcosθ - 1}/{sinθcosθ}

=> 2sinθcosθ/sinθcosθ

=> 2



hence, (1 + cot θ - cosec θ)(1 + tan θ + sec θ) = 2


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THANKS