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(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 |
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Answer» (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 ± \(\frac{\pi}{6}\) |
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