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If \frac{3 \pi}{4}<\alpha<\pi, then  \sqrt{\csc ^{2} \alpha+2 \cot \alpha}  is equal to be?

Option: 1

1+ \cot \alpha


Option: 2

-1-\cot \alpha


Option: 3

-1+\cot \alpha


Option: 4

1-\cot \alpha


Answers (1)

best_answer

\\\sqrt{\csc ^2 \alpha + 2 \cot \alpha }\\\\=\sqrt{1+cot^2 \alpha+ 2\cot \alpha}\\ \\=\sqrt{(1+\cot \alpha)^2}\\\\ =|1+\cot \alpha|\\\\ \because \text{Given } \frac{3\pi}{4} \leq \alpha \leq \pi \\ \cot \alpha \leq -1\\ |1+\cot \alpha| = -(1+\cot \alpha)

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sudhir.kumar

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