Question

sin (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 got this question during an online interview.

My question comes from Trigonometric Functions of Sum and Difference of Two Angles-1 topic in chapter Trigonometric Functions of Mathematics – Class 11

Answer 1

The correct option is (b) (\(\sqrt{3}\) + 1)/2\(\sqrt{2}\)

The explanation: sin (75°) = sin (45°+30°) = sin45° cos30° + cos45° sin30°

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

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