Question

2 sin 75° sin15° =_____________________________

(a) \(\frac{\sqrt{3}}{2}\)

(b) \(\frac{\sqrt{2}}{\sqrt{3}}\)

(c) \(\frac{1}{2}\)

(d) \(\frac{1}{\sqrt{2}}\)

This question was addressed to me in my homework.

I need to ask this question from Trigonometric Functions of Sum and Difference of Two Angles-2 topic in section Trigonometric Functions of Mathematics – Class 11

Answer 1

The correct choice is (c) \(\frac{1}{2}\)

The explanation: We know, 2 sin x sin y = cos (x – y) – cos (x + y)

2 sin 75° sin15° = cos (75°-15°) – cos (75°+15°)

= cos 60° – cos 90° = 1/2 – 0 = 1/2.