Solve for A .
2sin²2A + sin2A -1 = 0
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2 sin²2A + sin2A - 1 = 0
⇒ 2 sin²2A + 2 sin2A - sin2A - 1 = 0
⇒ 2 sin2A ( sin2A + 1 ) - 1 (sin2A + 1) = 0
⇒ ( 2sin2A - 1 )( sin2A + 1) = 0
sin2A = 1/2
⇒ 2A = 30° or 150° .
A = 15° or 75°.
sin 2A = -1
A = 135°.
If you want general solution then :
A = nπ + (-1)^n π/12 ,
A = nπ + (-1)^n 5π/12 .
A = (4n + 3)π/2
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