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Question
Prove that:
(cosec θ - sinθ )(secθ - cosθ ) ( tanθ +cot θ) =1
Solution
Taking LHS
(cosec θ - sinθ )(secθ - cos θ ) ( tanθ +cot θ)
`(1/(sin theta )- sin theta )(1/(cos θ )- cosθ )((sin θ)/(cos θ) +(cos θ)/(sin θ))`
`=((1-sin^2 θ)/(sin θ)) ((1- cos ^2θ)/(cos θ)) ((sin^2 θ + cos^2 θ)/(sin θ . cos θ))`
`= (cos^2 θ)/( sin θ) xx (sin^2 θ)/(cos θ ) xx 1/(sinθ . cos θ )` = 1 = RHS
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