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Prove the Following Trigonometric Identities. ((1 + Cot^2 Theta) Tan Theta)/Sec^2 Theta = Cot Theta - CBSE Class 10 - Mathematics

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Question

Prove the following trigonometric identities.

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

Solution

We have to prove `((1 + cot^2 theta) tan theta)/sec^2 theta = cot theta`

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

So

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

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

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

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

`= 1/tan theta`

`= cot theta`

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Solution Prove the Following Trigonometric Identities. ((1 + Cot^2 Theta) Tan Theta)/Sec^2 Theta = Cot Theta Concept: Trigonometric Ratios of Complementary Angles.
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