If 2 sin x = √3, evaluate. (i) 4 sin3 x - 3 sin x. (ii) 3 cos x - 4 cos3 x.

(i) ⇒ sin x = Taking cube on both sides, we get Now, 4 sin3 x - 3 sin x Hence, 4 sin3 x - 3 sin x = 0. (ii) sin x = sin x = ∴ If length of AB = a unit, length of AC = 2a unit. In Δ ABC, ⇒ AC2 = AB2 \+ BC2 (∵ AO is hypotenuse) ⇒ (2a)2 = \+ BC2 ⇒ 4a2 = 3a2 \+ BC2 ⇒ BC2 = 4a2 \- 3a2 ⇒ BC2 = a2 ⇒ BC = ⇒ BC = a cos x = Taking cube on both sides, we get Now, 3 cos x - 4 cos3 x Hence, 3 cos x - 4 cos3 x = 1.

If sec (90° - 3A).cos 48° = 1 and 0 ≤ 3A ≤ 90°; find the value of angle A.

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In △ABC, angle C is 90° then find the value of sin (A + B).

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If sec A sin A = 0, find the value of cos A.

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Find angle A, if sec 2A = cosec (A + 48°).

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Mathematics

If 2 sin x = √3, evaluate. (i) 4 sin3 x - 3 sin x. (ii) 3 cos x - 4 cos3 x.

Trigonometric Identities

Related Questions

If sec (90° - 3A).cos 48° = 1 and 0 ≤ 3A ≤ 90°; find the value of angle A.

In △ABC, angle C is 90° then find the value of sin (A + B).

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