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Prove the Following Trigonometric Identities. ((1 + Tan^2 Theta)Cot Theta)/((Cosec^2 Theta = Tan Theta

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Question

Prove the following trigonometric identities.

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

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Solution

We need to prove `((1 + tan^2 theta)cot theta)/(cosec^2 theta)   = tan theta`

Solving the L.H.S, we get

`((1 + tan^2 theta)cot theta)/(cosec^2 theta) = (sec^2 theta (cot theta))/(cosec^2 theta)`

Using `sec theta = 1/cos theta, cot theta = cos theta/sin theta`. `cosec theta = 1/sin theta` we get

`(sec^2 theta(cot theta))/(cosec^2 theta) = (1/cos^2 theta (cos theta/sin theta))/(1/sin^2 theta)`

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

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

`= sin theta/cos theta`

`= tan theta`

Hence proved.

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Chapter 11: Trigonometric Identities - Exercise 11.1 [Page 44]

APPEARS IN

R.D. Sharma Mathematics [English] Class 10
Chapter 11 Trigonometric Identities
Exercise 11.1 | Q 33 | Page 44

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