Question

If $A$ and $B$ are complementary angles, $\cot A\cdot \tan B$ is equal to?

• A. tan A.tan B
• B. cot A.cot B
• C. tan B.cot A
• D. sin A.cos B

Answer 1

Answer: (C)

Given: $A+B={90}^{\circ }$

Case I: $A={90}^{\circ }-B$

$\Rightarrow \cot A=\cot ({90}^{\circ }-B)=\tan B$

Hence, $\cot A\cdot \tan B=\tan B\times \tan B={\tan }^{2}B$

Case II: $B={90}^{\circ }-A$

$\Rightarrow \tan B=\tan ({90}^{\circ }-A)=\cot A$

Hence, $\cot A\cdot \tan B=\cot A\times \cot A={\cot }^{2}A$

Case III: $A={90}^{\circ }-B$ and $B={90}^{\circ }-A$

Therefore, $\cot B=\tan A$ and $\tan A=\cot B$

Hence, $\cot A\cdot \tan B=\tan B\cdot \cot A$