Solve for x :
sin2 x + sin2 30° = 1
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⇒sin 2x+(12)2=1⇒sin 2x+(14)=1⇒sin 2x=1−(14)⇒sin 2x=44−14⇒sin 2x=4−14⇒sin 2x=34⇒sin x=34⇒sin x=32⇒sin x=sin 60°⇒ \text{sin }^2 x + \Big(\dfrac{1}{2}\Big)^2 = 1\\[1em] ⇒ \text{sin }^2 x + \Big(\dfrac{1}{4}\Big) = 1\\[1em] ⇒ \text{sin }^2 x = 1 - \Big(\dfrac{1}{4}\Big)\\[1em] ⇒ \text{sin }^2 x = \dfrac{4}{4} - \dfrac{1}{4}\\[1em] ⇒ \text{sin }^2 x = \dfrac{4 - 1}{4}\\[1em] ⇒ \text{sin }^2 x = \dfrac{3}{4}\\[1em] ⇒ \text{sin } x = \sqrt\dfrac{3}{4}\\[1em] ⇒ \text{sin } x = \dfrac{\sqrt3}{2}\\[1em] ⇒ \text{sin } x = \text{sin } 60°\\[1em]⇒sin 2x+(21)2=1⇒sin 2x+(41)=1⇒sin 2x=1−(41)⇒sin 2x=44−41⇒sin 2x=44−1⇒sin 2x=43⇒sin x=43⇒sin x=23⇒sin x=sin 60°
So, x = 60°
Hence, x = 60°.
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3 tan2 (2x - 20°) = 1
cos(x2+10°)cos\Big(\dfrac{x}{2} + 10°\Big)cos(2x+10°) = 32\dfrac{\sqrt3}{2}23
cos2 30° + cos2 x = 1
cos2 30° + sin2 2x = 1
