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Prove the Following Trigonometric Identities. Tan Theta + 1/Tan Theta = Sec Theta Cosec Theta - Mathematics

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Question

Prove the following trigonometric identities.

`tan theta + 1/tan theta = sec theta cosec theta`

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Solution

We know that `sec^2 theta - tan^2 theta = 1`

So,

`tan theta + 1/tan theta = (tan^2 theta + 1)/tan theta`

`= sec^2 theta/tan theta`

`= sec theta sec theta/tan theta`

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

`= sec theta cosec theta`

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Chapter 11: Trigonometric Identities - Exercise 11.1 [Page 43]

APPEARS IN

RD Sharma Mathematics [English] Class 10
Chapter 11 Trigonometric Identities
Exercise 11.1 | Q 6 | Page 43

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