Question

Simplify (1 – cosθ) (1 + cosθ) (1 + cot^2 θ)

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Answer 1

Heya!

Here is ur answer...

= (1-cosΦ)(1+cosΦ)(1+cot²Φ)

= (1-cos²Φ) (1+cot²Φ)

= (sin²Φ) (cosec²Φ)

= (sinΦ • cosecΦ)²

= 1²

= 1

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Identities used :

=> 1-cos²Φ = sin²Φ

=> 1+cot²Φ = cosec²Φ

=> (a+b)(a-b) = a²-b²

Hope it helps u..