Question

sin(15°) =_________________

(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\(\sqrt{2}\)

The question was posed to me by my school principal while I was bunking the class.

My question is based upon Trigonometric Functions of Sum and Difference of Two Angles-1 in division Trigonometric Functions of Mathematics – Class 11

Answer 1

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

The best I can explain: sin (15°) = 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\(\sqrt{2}\).