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If x lies in third quadrant, then the expression \sqrt{3-\sqrt{\frac{1}{1+\cot^2x}}} equals

Option: 1

\sqrt{3+cos(x)}


Option: 2

\sqrt{3-cos(x)}


Option: 3

\sqrt{3-sin(x)}


Option: 4

\sqrt{3+sin(x)}


Answers (1)

best_answer

\\\sqrt{3-\sqrt{\frac{1}{1+\cot^2x}}}\\ =\sqrt{3-\sqrt{\frac{1}{\csc ^2x}}}\\ =\sqrt{3-|\sin x|}

Now as x lies in third quadrant, so sin(x) < 0, and thus |sin(x)| = - sin(x)

So the given expression equals

\\\sqrt{3+sin(x)}

Posted by

Shailly goel

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