The value of $\sin 15^\circ \cos 15^\circ$ is : (a) $\dfrac{\sqrt{3}}{2}$ (b) $1$ (c) $\dfrac{1}{4}$ (d) $\dfrac{1}{2}$

The value of sin 15^° cos 15^° is : (a) dfrac√(3)2 (b) 1 (c) (1)/(4) (d) (1)/(2)

Question 25 of 36

\sin 15^\circ \cos 15^\circ

(a)

\dfrac{\sqrt{3}}{2}

(b)

1

(c)

\dfrac{1}{4}

(d)

\dfrac{1}{2}

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$\sin15^\circ\cos15^\circ = \tfrac12\sin30^\circ = \tfrac12\cdot\tfrac12 = \tfrac14$ , so the answer is option (c).

Recall the double-angle formula

$\sin 2\theta = 2\sin\theta\cos\theta \;\Rightarrow\; \sin\theta\cos\theta = \frac{1}{2}\sin 2\theta.$

With $\theta = 15^\circ$ :

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