Question

2 cos 75° cos 15° =____________________

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

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

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

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

I have been asked this question in a national level competition.

Question is from Trigonometric Functions of Sum and Difference of Two Angles-2 in portion Trigonometric Functions of Mathematics – Class 11

Answer 1

Right choice is (b) \(\frac{1}{2}\)

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

2 cos 75° cos 15° = cos (75°+15°) + cos (75°-15°)

= cos 90° + cos 60°

= 0 + 1/2 = 1/2.