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Mathematics

Find value of x, if :

cos(2x - 6°) = cos2 30° - cos2 60°

Trigonometric Identities

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Answer

Solving,

⇒ cos(2x - 6°) = cos2 30° - cos2 60°

⇒ cos(2x - 6°) = (32)2−(12)2\Big(\dfrac{\sqrt{3}}{2}\Big)^2 - \Big(\dfrac{1}{2}\Big)^2

⇒ cos(2x - 6°) = 34−14\dfrac{3}{4} - \dfrac{1}{4}

⇒ cos(2x - 6°) = 24\dfrac{2}{4}

⇒ cos(2x - 6°) = 12\dfrac{1}{2}

⇒ cos(2x - 6°) = cos 60°

⇒ 2x - 6° = 60°

⇒ 2x = 66°

⇒ x = 33°.

Hence, x = 33°.

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