Question

If $\frac{3\pi }{4}<\alpha <\pi$ then $\sqrt{{\text{cosec}}^2\alpha +2\cot \alpha }=$

• A. $1-\cot \alpha$
• B. $-1+\cot \alpha$
• C. $1+\cot \alpha$
• D. $-1-\cot \alpha$

Answer 1

Answer: (D)

$\sqrt{1+{\cot }^2\alpha +2\cot \alpha }=\sqrt{(1+\cot \alpha {)}^2}=|1+\cot \alpha |$
When $\frac{3\pi }{4}<\alpha <\pi ,\cot \alpha <-1$ (by graph)