First slide

Trignometry

Question

Find value of sin² 15º + sin² 645º :

Easy

A

$\frac{1}{2}$
B

1
C

$\frac{1}{\sqrt{3}}$
D

None of these

Solution

$\sin^{2} 15^{\circ} + \sin^{2} (645^{\circ})$
$\begin{array}{l} Now, \sin (645^{\circ}) = \sin (7 \times 90 + 15^{\circ}) \\ = - \cos 15^{\circ} \\ So, \sin^{2} 15^{\circ} + {(- \cos 15^{\circ})}^{2} = \sin^{2} 15^{\circ} + \cos^{2} 15^{\circ} = 1 . \end{array}$

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