If 4 cos2 x = 3 and x is an acute angle; find the value of : (i) x (ii) cos2 x + cot2 x (iii) cos 3x (iv) sin 2x

Question

KnowledgeBoat · Accepted Answer

(i) 4 cos2 x = 3 ⇒ cos2 x = ⇒ cos x = ⇒ cos x = ⇒ cos x = cos 30° Hence, x = 30°. (ii) cos x = cos 30° = cot x = cot 30° = Now, cos2 x + cot2 x Hence, cos2 x + cot2 x = . (iii) cos 3x = cos (3 x 30°) = cos 90° = 0 Hence, cos 3x = 0. (iv) sin 2x = sin (2 x 30°) = sin 60° = Hence, sin 2x = .

Mathematics

If 4 cos² x = 3 and x is an acute angle; find the value of :
(i) x
(ii) cos² x + cot² x
(iii) cos 3x
(iv) sin 2x

Trigonometric Identities

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