Question

sec

Prove that sec square theta + cosec square theta is equal to sec squared theta into cosec squared theta. ​

Answer 1

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sec2θ+cosec2θ=sec2θ.cosec2θ 

L.H.S.

\begin{lgathered}= \frac{1}{ {cos}^{2} \theta} + \frac{1}{ {sin}^{2} \theta} \\ = \frac{ {sin}^{2} \theta \: + {cos}^{2} \theta}{ {cos}^{2} \theta. {sin}^{2} \theta } \\ = \frac{1}{ {cos}^{2} \theta. {sin}^{2} \theta } \\ = {sec}^{2} \theta. {cosec}^{2} \theta\end{lgathered}=cos2θ1+sin2θ1=cos2θ.sin2θsin2θ+cos2θ=cos2θ.sin2θ1=sec2θ.cosec2θ 

= R.H.S.

Hence, proved.

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