Question

if 2.sin 2teta =root3, then prove that 3 cotsquare teta-2 sin teta=8​

Answer 1

$\huge\underline\mathfrak\red{Answer}$

$2. \sin2 \alpha = \sqrt{3} \\ \\ \sin2 \alpha = \frac{ \sqrt{3} }{2} \\ \\ \sin60 = \frac{ \sqrt{3} }{2} \\ \\ \sin2 \alpha = \sin \frac{\pi}{3} \\ \\ 2 \alpha = \frac{\pi}{3} \\ \\ \alpha = \frac{\pi}{6} ....(1)$

$3 {cot}^{2} \alpha - 2 \sin \alpha \\ \\ we \: know \: that \: \alpha = \frac{\pi}{6} \\ \\ 3 {cot}^{2} \frac{\pi}{6} - 2 \sin \frac{\pi}{6} \\ \\ 3 ( \sqrt{3} )^{2} - 2( \frac{ 1}{2} ) \\ \\ {3} \times {3} - 1 \\ \\ 9 - 1 = 8$

Answer 2

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