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1 + Tan 2 a 1 + Cot 2 a is Equal to - Mathematics

MCQ

\[\frac{1 + \tan^2 A}{1 + \cot^2 A}\]is equal to

Options

  •  sec2 A

  • −1

  •  cot2 A

  •  tan2 A

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Solution

Given:

`(1+tan^2 A)/(1+cot^2 A)`

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

`=(cos^2 A+sin^2 A/cos^2 A)/(sin^2 A+cos^2 A/sin^2A)`

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

`= tan^2 A`

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 11 Trigonometric Identities
Q 28 | Page 58
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