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Prove the Following Trigonometric Identities. (1 - Cos Theta)/Sin Theta = Sin Theta/(1 + Cos Theta) - Mathematics

Prove the following trigonometric identities.

`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`

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Solution

We have to prove `(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`

We know that, `sin^2 theta + cos^2 theta = 1`

Multiplying both numerator and denominator by `(1 + cos theta)`, we have

`(1 - cos theta)/sin theta = ((1 - cos theta)(1 + cos theta))/(sin theta(1 + cos theta))`

`= (1 - cos^2 theta)/(sin theta(1 + cos theta))`

` = (sin^2 theta)/(sin theta(1 + cos theta))`

`= sin theta/(1 + cos theta)`

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 11 Trigonometric Identities
Exercise 11.1 | Q 12 | Page 43
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