Question

Trigonometry:-

prove

(1+cos theta) (1-cos theta) (1+cot² theta) =1​

Answer 1

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Answer 2

Proof:-

(1+cos theta) (1-cos theta) (1+cot² theta) =1​

LHS

(1+cos theta) (1-cos theta) (1+cot² theta) [(a+b)(a-b=a^2-b^2)]

=(1-cos^2theta)(1+cot² theta) [identity used:- sin^2theta+cos^2theta=1]

=(sin^2theta)(1+cot² theta) [identity used :- 1+cot^2theta=cosec^2theta]

=(sin^2theta)(cosec^2theta)

=sin^2theta x 1/sin^2theta

=1

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