Question

Prove: under root (sec theta-1/sec theta+1) + under root (sec theta+1/sec theta-1) = 2 Cosec theta?pleaseee explain with clear steps!!!asap!!!!

Answer 1

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Answer 2

Answer:

$\sqrt{\frac{sec\theta-1}{sec\theta+1}}+\sqrt{\frac{sec\theta-1}{sec\theta+1}}= 2cosec\theta$

Step-by-step explanation:

$LHS=\sqrt{\frac{sec\theta-1}{sec\theta+1}}+\sqrt{\frac{sec\theta-1}{sec\theta+1}}$

$=\frac{\left(\sqrt{sec\theta-1}\right)^{2}+\left(\sqrt{sec\theta+1}\right)^{2}}{\sqrt{(sec\theta+1)(sec\theta-1)}}$

$=\frac{sec\theta-1+sec\theta+1}{\sqrt{sec^{2}\theta-1^{2}}}$

$=\frac{2sec\theta}{\sqrt{tan^{2}\theta}}$

$=\frac{2sec\theta}{tan\theta}$

$=\frac{\frac{2}{cos\theta}}{\frac{sin\theta}{cos\theta}}$

$=\frac{2}{sin\theta}\\=2cosec\theta\\=RHS$

Therefore,

$\sqrt{\frac{sec\theta-1}{sec\theta+1}}+\sqrt{\frac{sec\theta-1}{sec\theta+1}}= 2cosec\theta$

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