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प्रश्न
\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to
विकल्प
2 tan θ
2 sec θ
2 cosec θ
2 tan θ sec θ
उत्तर
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`
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