If sin 30° = a, then find \(\frac{sin 120° - cos 150°}{tan 210°}\) ?

\(\frac{2(1- a^2)}{a}\)

sin(120°) = sin (90° + 30°) = cos 30°

cos (150°) = cos (180° - 30°) = - cos 30°

tan (180° + 30°) = tan 30°

⇒ \(\frac{cos 30° + cos 30°}{tan 30°}\) = \(\frac{2 cos 30°}{tan 30°}\) = \(\frac{2cos^2 30°}{sin 30°}\)

(sin² 30° = a² ⇒ cos² 30° = 1 - a²)

Hence,

\(\frac{2cos^2 30°}{sin 30°}\) = \(\frac{2(1 - a^2)}{a}\)