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

cos-75deg-cos-15deg-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/\(\sqrt{2}\).