Prove the following: tan ( 90 ° − θ ) cot θ cosec 2 θ = cos2θ - Mathematics

Prove the following: `(tan(90° - θ)cotθ)/("cosec"^2 θ)` = cos²θ

Sum

L.H.S.

= `(tan(90° - θ)cotθ)/("cosec"^2 θ)`

= `(cotθ xx cotθ)/("cosec^2 θ)`

= `(cot^2 θ)/("cosec"^2 θ)`

= `((cos^2 θ)/(sin^2 θ))/((1)/(sin^2 θ)`

= cos²θ
= R.H.S.

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Trigonometric Equation Problem and Solution

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Chapter 27: Trigonometrical Ratios of Standard Angles - Exercise 27.3

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