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Tan θ Sec θ − 1 + Tan θ Sec θ + 1 is Equal to - Mathematics

MCQ

\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to 

Options

  • 2 tan θ

  •  2 sec θ

  •  2 cosec θ

  •  2 tan θ sec θ

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Solution

The given expression is  `tan θ /(secθ-1)+tan θ/(sec θ+1)`

=` (tan θ (sec θ+1)+tan θ(secθ-1))/((secθ-1)(secθ+1))`

= `(tan θ sec θ+tanθ+tan θ secθ-tan θ)/(sec^2θ-1)`

=`( 2tanθ secθ)/tan^2θ`

=`(2secθ)/tan θ` 

= `(2 1/cos θ)/(sinθ/cos θ)` 

=`2 1/ sinθ`

= `2 cosec θ`

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 11 Trigonometric Identities
Q 10 | Page 57
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