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

Prove the following trigonometric identities.

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

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Solution

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

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

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

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

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

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

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

`= cosec theta  + cot 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 13 | Page 44
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