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Question Number 211575 by BaliramKumar last updated on 13/Sep/24

Answered by som(math1967) last updated on 13/Sep/24

$$\left(\mathit{a}\right)\frac{1}{2}(\mathit{m}+\mathit{n}+\frac{1}{\mathit{m}}+\frac{1}{\mathit{n}})$$

Answered by A5T last updated on 13/Sep/24

$${sec}^2\theta -{tan}^2\theta =(sec\theta -tan\theta )(sec\theta +tan\theta )=1$$$$\Rightarrow sec\theta +tan\theta =\frac{1}{n}$$$${cosec}^2\theta -{cot}^2\theta =(cosec\theta -cot\theta )(cosec\theta +cot\theta )=1$$$$\Rightarrow cosec\theta +cot\theta =\frac{1}{m}$$$$\Rightarrow \frac{1}{2}(m+n+\frac{1}{m}+\frac{1}{n})=cosec\theta +sec\theta \Rightarrow \left(a\right)$$

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