cos 75° – cos 15° =___________________ A. $$\frac{\sqrt{3}}{\sqrt{2}}$$

cos 75° – cos 15° =___________________

A. $$\frac{\sqrt{3}}{\sqrt{2}}$$

B. $$\frac{\sqrt{2}}{\sqrt{3}}$$

C. $$\frac{1}{\sqrt{2}}$$

D. –$$\frac{1}{\sqrt{2}}$$

The question was asked in unit test.

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

Right choice is D. –$$\frac{1}{\sqrt{2}}$$

The explanation: cos x – cos y = – 2 sin (x+y)/2 sin (x-y)/2

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

= – 2 sin 45° sin 30°

= – 2*1/$$\sqrt{2}$$*1/2= – 1/$$\sqrt{2}$$.