Question 72

Simplify: $$\sin 15^\circ \sin 75^\circ + \cos 75^\circ \cos 15^\circ$$

Solution

Use

cos(a - b) = cos a cos b + sin a sin b

So,

$$ \cos 75^\circ \cos 15^\circ + \sin 15^\circ \sin 75^\circ = \cos(75^\circ - 15^\circ) $$

$$ \cos(75^\circ - 15^\circ) = \cos 60^\circ = \frac{1}{2} $$

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