Question

sin 75° + sin 15° = _________________

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

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

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

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

This question was addressed to me by my school principal while I was bunking the class.

My doubt stems from Trigonometric Functions of Sum and Difference of Two Angles-2 in section Trigonometric Functions of Mathematics – Class 11

Answer 1

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

For explanation I would say: We know, sin x + sin y = 2 sin (x+y)/2 cos (x-y)/2

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

= 2 sin 45° cos 30°

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