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Trigonometric Ratios Of Multiple And Sub Multiple Angles — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Ratios Of Multiple And Sub Multiple Angles1 Mark
Question
If $12\sin\text{x}-9\sin^2\text{x}$ attains its maximum value at $\text{x}=\alpha,$ then write the value of $\sin\alpha.$
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Answer

$12\sin\text{x}-9\sin^2\text{x}$ has maximum value as 4, so $12\sin\alpha-9\sin^2\alpha=4$ $9\sin^2\alpha-612\sin\alpha+4=0$ $9\sin^2\alpha-6\sin\alpha-6\sin\alpha+4=0$ $3\sin\alpha(3\sin\alpha-2)-2(3\sin\alpha-2)=0$ $(3\sin\alpha-2)(3\sin\alpha-2)=0$$3\sin\alpha-2=0$
$\sin\alpha=\frac23$

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