Solve for x :
cos2 30° + cos2 x = 1
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⇒(32)2+cos 2x=1⇒(34)+cos 2x=1⇒cos 2x=1−(34)⇒cos 2x=44−34⇒cos 2x=4−34⇒cos 2x=14⇒cos x=14⇒cos x=12⇒cos x=cos 60°⇒ \Big(\dfrac{\sqrt{3}}{2}\Big)^2 + \text{cos }^2 x = 1\\[1em] ⇒ \Big(\dfrac{3}{4}\Big) + \text{cos }^2 x = 1\\[1em] ⇒ \text{cos }^2 x = 1 - \Big(\dfrac{3}{4}\Big)\\[1em] ⇒ \text{cos }^2 x = \dfrac{4}{4} - \dfrac{3}{4}\\[1em] ⇒ \text{cos }^2 x = \dfrac{4 - 3}{4}\\[1em] ⇒ \text{cos }^2 x = \dfrac{1}{4}\\[1em] ⇒ \text{cos } x = \sqrt\dfrac{1}{4}\\[1em] ⇒ \text{cos } x = \dfrac{1}{2}\\[1em] ⇒ \text{cos } x = \text{cos 60°} \\[1em]⇒(23)2+cos 2x=1⇒(43)+cos 2x=1⇒cos 2x=1−(43)⇒cos 2x=44−43⇒cos 2x=44−3⇒cos 2x=41⇒cos x=41⇒cos x=21⇒cos x=cos 60°
So, x = 60°
Hence, x = 60°.
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cos(x2+10°)cos\Big(\dfrac{x}{2} + 10°\Big)cos(2x+10°) = 32\dfrac{\sqrt3}{2}23
sin2 x + sin2 30° = 1
cos2 30° + sin2 2x = 1
sin2 60° + cos2 (3x - 9°) = 1
