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Prove the Following Trigonometric Identities. (Cosecθ + Sinθ) (Cosecθ − Sinθ) = Cot2 θ + Cos2θ - Mathematics

Prove the following trigonometric identities.

(cosecθ + sinθ) (cosecθ − sinθ) = cot2 θ + cos2θ

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Solution

We have to prove  (cosecθ + sinθ) (cosecθ − sinθ) = cot2 θ + cos2θ

We know that

`sin^2 theta + cos^2 theta = 1`

`cosec^2 theta - cot^2 theta = 1`

So,

`(cosec theta + sin theta)(cosec theta - sin theta) = cosec^2 theta -  sin^2 theta`

`= (1 + cot^2 theta) - (1 - cos^2 theta)`

`= 1 + cot^2 theta  - 1 + cos^2 theta`

`= cot^2 theta + cos^2 theta`

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 11 Trigonometric Identities
Exercise 11.1 | Q 15 | Page 44
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