Question

If $\cot A=\frac{3}{4}$ what is the value of $\frac{\sin A+\cos A}{\sin A-\cos A}$?

• A. $3$
• B. $4$
• C. $5$
• D. $7$

Answer 1

Answer: (D)

$7$

$cotA=\frac{3}{4}=\frac{B}{P}$

$H^2=B^2+P^2$

$\Rightarrow H=\sqrt{3^2+4^2}$

$\Rightarrow H=\sqrt{9+16}$

$\Rightarrow H=\sqrt{25}=5m$

$\therefore sinA=\frac{P}{H}=\frac{4}{5}$ and $cosA=\frac{B}{H}=\frac{3}{5}$

$\frac{sinA+cosA}{sinA-cosA}=\frac{\frac{4}{5}+\frac{3}{5}}{\frac{4}{5}-\frac{3}{5}}$

$\Rightarrow \frac{\frac{7}{5}}{\frac{1}{5}}=7$