Question

The value of $\frac{\cos ({90}^o-A)}{\text{cosec}({90}^o-A)}\times \frac{\cot ({90}^o-A)}{\sin A}$ is

• A. $\cos A$
• B. $\sin A$
• C. $\tan A$
• D. $\sec A$

Answer 1

Answer: (B)

$\sin A$

The value of $\frac{\cos ({90}^o-A)}{\text{cosec}({90}^o-A)}\times \frac{\cot ({90}^o-A)}{\sin A}$ is equal to

$=\frac{\sin A}{\sec A}\times \frac{\tan A}{\sin A}$

$=\frac{\tan A}{\sec A}$

$=\frac{\frac{\sin A}{\cos A}}{\frac{1}{\cos A}}$

$=\sin A$