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Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

cos2 30∘ + si...

Question

$c o s^{2} 30^{\circ} + s i n^{2} 2 x = 1$

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Solution

$c o s^{2} 30 + s i n^{2} 2 x = 1$
$s i n^{2} 2 x + (\frac{\sqrt{3}}{2})^{2} = 1$
$s i n^{2} 2 x = 1 - \frac{3}{4}$
${sin}^{2} 2 x = \frac{1}{4}$
$sin 2 x = \frac{1}{2}$
$sin 2 x = sin 30$
$2 x = 30^{\circ}$
$x = 15^{\circ}$

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