If 3- 4 - - then - 2- - 1 -sin 2 - is equal to

The correct option is B 1 α #160; #160;√( 2α #160; + 1 /sin ^ 2 α #160; #160; #160;) =√( 2α #160; + cosec ^ 2 α #160; #160;) =√ ...

If 3π/ 4 <α...

Question

If $\frac{3 π}{4} < α < π$ , then $\sqrt{2 cot α + \frac{1}{{sin}^{2} α}}$ is equal to

1 - cot α

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1 + cot α

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- 1 + cot α

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- 1 - cot α

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Solution

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\frac{3 π}{4} < α < π

\sqrt{2 cot α + \frac{1}{{sin}^{2} α}}

(\frac{1}{{sec}^{2} α - {cos}^{2} α} + \frac{1}{csc^{2} α - {sin}^{2} α}) \times {sin}^{2} α {cos}^{2} α = \frac{1 - {sin}^{2} α {cos}^{2} α}{2 + {sin}^{2} α {cos}^{2} α}

3 π / 4 < α < π

\sqrt{2 cot α + \frac{1}{{sin}^{2} α}}

c o s^{6} α + s i n^{6} α + K s i n^{2} 2 α = 1,

y (α) = \sqrt{2 (\frac{tan α + cot α}{1 + {tan}^{2} α}) + \frac{1}{{sin}^{2} α}}

α \in (\frac{3 π}{4}, π)

\frac{d y}{d α}

α = \frac{5 π}{6}