Question

Pls help! Its urgent

Answer 1

Answer:

$\sqrt{\left(1-\cos ^2\left(\phi\right)\right)\sec ^2\left(\phi\right)}=\tan \left(\phi\right)$

Step-by-step explanation:

$\sqrt{\left(1-\cos ^2\left(\phi\right)\right)\sec ^2\left(\phi\right)}$

$\gray{\sqrt{\left(1-\cos ^2\left(\phi\right)\right)\sec ^2\left(\phi\right)}}$

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

$\gray{\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0}$

$\gray{\sqrt{\sec ^2\left(\phi\right)}=\sec \left(\phi\right)}$

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

$\gray{\mathrm{Use\:the\:following\:identity}:\quad \cos ^2\left(x\right)+\sin ^2\left(x\right)=1}$

$\gray{\mathrm{Therefore\:}1-\cos ^2\left(x\right)=\sin ^2\left(x\right)}$

$=\sqrt{\sin ^2\left(\phi\right)}\sec \left(\phi\right)$

$\gray{\sqrt{\sin ^2\left(\phi\right)}=\sin \left(\phi\right)}$

$=\sin \left(\phi\right)\sec \left(\phi\right)$

$\gray{\mathrm{Use\:the\:following\:identity:}\:\sec \left(x\right)=\dfrac{1}{\cos \left(x\right)}}$

$\gray{\mathrm{Use\:the\:following\:identity:}\:\dfrac{\sin \left(x\right)}{\cos \left(x\right)}=\tan \left(x\right)}$

$=\tan \left(\phi\right)$

Answer 2

Answer:

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