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  • sqroot (1-cos power theta) sec power 2 theta = tan theta

Prove that \sqrt{\left ( 1-\cos ^{2}\theta \right )\sec ^{2}\theta }= \tan \theta

Answers (1)

   
L.H.S

 \sqrt{\left ( 1-\cos ^{2}\theta \right )\sec ^{2}\theta } \cdots \left ( 1 \right )
   We know that
1-\cos ^{2}\theta = \sin ^{2}\theta\text{ in (1)}
\sqrt{\sin ^{2}\theta \cdot \sec ^{2}\theta }
=\sqrt{\sin ^{2}\theta \times \frac{1}{\cos ^{2}\theta } }             \left ( \because \sec \theta = \frac{1}{\cos \theta } \right )
=\sqrt{\frac{\sin ^{2}\theta }{\cos ^{2}\theta }}
=\sqrt{\tan ^{2}\theta }= \tan \theta                   \left ( \because \frac{\sin \theta }{\cos \theta }= \tan \theta \right )

L.H.S. = R.H.S.

Hence the given expression is true.

 

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infoexpert27

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