Question

cos 75° + cos 15° =___________________

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

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

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

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

The question was asked in a job interview.

The question is from Trigonometric Functions of Sum and Difference of Two Angles-2 in chapter Trigonometric Functions of Mathematics – Class 11

Answer 1

Correct choice is (a) \(\frac{\sqrt{3}}{\sqrt{2}}\)

Explanation: We know, cos x + cos y = 2 cos (x+y)/2 cos (x-y)/2

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

= 2 * cos 45° * cos30°

= 2*(1/\(\sqrt{2}\))*(\(\sqrt{3}\)/2)

= \(\sqrt{3}\)/\(\sqrt{2}\).