Simplify the following :

\(\rm {\cos X -\sqrt{3} \sin X\over 2}\)

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 03 Dec 2022 Shift 3)

Answer 1

Given:

\(\rm {\cos X -\sqrt{3} \sin X\over 2}\)

Concept used:

cos(x + y) = cos x × cos y - sin x × sin y

π = 180°

Trigo

Calculation:

\(\rm {\cos X -\sqrt{3} \sin X\over 2}\)

⇒ \(\frac {1}{2} × cos X - \frac {\sqrt3}{2} × sin X\)

⇒ \(cos 60^\circ × cos X - sin 60^\circ× sin X\)

⇒ cos(60° + X)

⇒ Cos (\( { π{} \over 3} + X\))

∴ The simplified value is Cos (\( { π{} \over 3} + X\)).