Question

cos(75°) =__________________

(a) (1 – \(\sqrt{3}\))/2\(\sqrt{2}\)

(b) (\(\sqrt{3}\) + 1)/2\(\sqrt{2}\)

(c) (\(\sqrt{3}\) – 1)/2\(\sqrt{2}\)

(d) (-\(\sqrt{3}\) – 1)/2\(\sqrt{2}\)

I have been asked this question in examination.

My doubt stems from Trigonometric Functions of Sum and Difference of Two Angles-1 topic in portion Trigonometric Functions of Mathematics – Class 11

Answer 1

Correct choice is (c) (\(\sqrt{3}\) – 1)/2\(\sqrt{2}\)

To elaborate: cos(75°) = cos (45°+30°) = cos45° cos30° – sin45° sin30°

= (1/\(\sqrt{2}\) * \(\sqrt{3}\)/2) – (1/\(\sqrt{2}\) * 1/2) {cos(x + y)=cos x cos y – sin x sin y}

= (\(\sqrt{3}\) – 1)/2\(\sqrt{2}\).