Question : Find the value of the following expression $\frac{(1+\sec\phi)}{\sec\phi}(1-\cos\phi)$.
Option 1: $\cos ^2 \phi$
Option 2: $\sec ^2 \phi$
Option 3: $\cot ^2 \phi$
Option 4: $\sin ^2 \phi$
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Correct Answer: $\sin ^2 \phi$
Solution :
Given: $\frac{(1+\sec\phi)}{\sec\phi}(1-\cos\phi)$
= $\frac{(1+\frac{1}{\cosØ})}{\frac{1}{\cos\phi}}(1-\cos\phi)$
= $\cos\phi\frac{(1+\cos\phi)}{\cos\phi}$$(1-\cos\phi)$
= $(1+\cos\phi)(1-\cos\phi)$
= $1-\cos^2\phi$
= $\sin^2\phi$
Hence, the correct answer is $\sin^2\phi$.
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