Question

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$\sqrt{sec^2\theta + cosec^2\theta}$=$tan\theta + cot\theta$​

Answer 1

Answer:

$\sqrt{sec^2\theta + cosec^2\theta}$

Taking L.H.S=$\sqrt{sec^2\theta +cosec^2\theta}$

$\implies$$\sqrt{(1+tan^2\theta)+(1+cot^2\theta}$

=$\sqrt{tan^2\theta+cot^2\theta+2}$

=$\sqrt{tan^2\theta+cot^2\theta+2tan\theta*cot\theta}$

$[\therefore tan\theta+cot\theta=1]$

=$\sqrt{(tan\theta+cot\theta)^2}$=${tan\theta+cot\theta}$=R.H.S PROVED