Question

Evaluate \[ \frac{\cot A+\tan B}{\cot B+\tan A}. \]

• A. \(\dfrac{\cot A}{\cot B}\)
• B. \(\dfrac{\cos A}{\sin B}\)
• C. \(\dfrac{\sin A}{\sin B}\)
• D. \(\cot A\cos B\)

Hint:

Whenever an expression contains both \(\tan\theta\) and \(\cot\theta\), replace \[ \boxed{\tan\theta=\frac1{\cot\theta}} \] or \[ \boxed{\cot\theta=\frac1{\tan\theta}} \] to simplify the expression.

Answer 1

The Correct Option is A