(i) If sin x = cos x, x ∈ [0, π] then is (a) 0 (b) π/4 (c) π/3 (d) π (ii) Write the following in ascending order of t its values, sin 100°, sin 0°

Question

(i) If sin x = cos x, x ∈ [0, π] then is

(a) 0

(b) \(\frac{\pi}{4}\)

(c) \(\frac{\pi}{3}\)

(d) \(\pi\)

(ii) Write the following in ascending order of t its values, sin 100°, sin 0°, sin 50°, sin 200°

(iii) Solve: sin2x – sin4x + sin6x = 0

Answer 1

(i) (b) \(\frac{\pi}{4}\)

(ii) sin 100° = sin(l 80 – 80) = sin 80°

sin 200° = sin(l 80° + 20°) = -sin 20°

The ascending order is

sin 200°, sin 0°, sin 50°, sin 100°

(iii) sin2x + sin6x – sin4x = 0

⇒ 2sin 4x cos2x – sin 4x = 0

⇒ sin 4x(2 cos 2x – 1) = 0

⇒ sin4x = 0 or (2cos2x – 1) = 0

⇒ 4x = nπ or cos2x = \(\frac{1}{2}\)

⇒ \(x = \frac{n \pi}{4}\)

⇒ cos 2x = \(\frac{\pi}{3}\)

⇒ \(x = \frac{n \pi}{4}\)

⇒ 2x = 2nπ ± \(\frac{\pi}{3}\)

⇒ \(x = \frac{n \pi}{4}\)

⇒ x = nπ ± \(\frac{\pi}{6}\)