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Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

The value of ...

Question

The value of $sin 105^{\circ} . sin 75^{\circ} i s$

A

\frac{\sqrt{3} + 2}{4}

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B

\frac{\sqrt{3} + 2}{2}

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C

\frac{\sqrt{3} - 2}{4}

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D

\frac{\sqrt{3} - 2}{2}

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Solution

The correct option is A $\frac{\sqrt{3} + 2}{4}$
$s i n 105^{\circ} = s i n (90^{\circ} + 15^{\circ}) = c o s 15^{\circ}$
$c o s 15^{\circ} = \frac{\sqrt{3} + 1}{2 \sqrt{2}}$
$s i n 75^{\circ} = s i n (90^{\circ} - 15^{\circ}) = c o s 15^{\circ}$
$c o s 15^{\circ} = \frac{\sqrt{3} + 1}{2 \sqrt{2}}$
$s i n 105^{\circ} . s i n 75^{\circ} = \frac{\sqrt{3} + 2}{4}$

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Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

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