Question

If A + B = 90°, the value of \[\frac{\cos A}{\sin B} \times \frac{\tan B}{\cot A}\] is ______.

Options

• 1

• 2

• sin A

• cos В

Answer 1

If A + B = 90°, the value of \[\frac{\cos A}{\sin B} \times \frac{\tan B}{\cot A}\] is 1.

Explanation:

Since A + B = 90°, we have cos A = sin B and tan B = cot A. Substituting these relationships into the expression gives:

\[\frac{\sin B}{\sin B} \times \frac{\cot A}{\cot A} = 1 \times 1 = 1\]