Question

please solve this question
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Answer 1

Answer:

A part

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Answer 2

Answer:

your solution is as follows

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Step-by-step explanation:

$to \: find : \\ value \: of \: sin \: x \\ \\ given \: trigonometric \: equation \: is \\ sin \: x + cos \: x = \sqrt{6} .sin \: x \\ \\ cos \: x = \sqrt{6} .sin \: x - sin \: x \\ \\ cos \: x = sin \: x( \sqrt{6} - 1) \\ \\ \frac{cos \: x}{sin \: x} = \sqrt{6} - 1 \\ \\ cot \: x = \sqrt{6} - 1 \\ \\ we \: know \: that \\ 1 + cot {}^{2} x = cosec {}^{2} x \\ \\ = 1 + ( \sqrt{6} - 1) { }^{2} \\ \\ = 1 + 6 + 1 - 2 \sqrt{6} \\ \\ = 8 - 2 \sqrt{6} \\ \\ cosec \: x = ±\sqrt{8 - 2 \sqrt{6} } \\ \\ sin \: x = ± \frac{1}{ \sqrt{8 - 2 \sqrt{6} } }$