Question

cosec²theta = 2cottheta
find out the value of theta.​

Answer 1

${ \csc}^{2} \alpha = 2 \cot \alpha \\ \\ = > \frac{1}{ { \sin}^{2} \alpha } = \frac{2 \cos \alpha }{ \sin\alpha } \\ \\ = > \frac{1}{2} = \sin \alpha \cos \alpha \\ \\ = > \sin \alpha \cos \alpha = \frac{1}{ \sqrt{2} } \times \frac{1}{ \sqrt{2} } \\ \\ = > \sin \alpha = \cos\alpha = \frac{1}{ \sqrt{2} } \\ \\ = > \alpha = 45 \\ \\ (\sin45 = \cos45 = \frac{1}{ \sqrt{2} } )$

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