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No. But sin2a equals 1 minus cos2a ... and ... cos2a equals 1 minus sin2a
sin2a=
The proof that sin2A plus sin2B plus sin2c equals 4sinAsinBsinC lies in the fact that (sin 2A + sin 2B + sin 2C) = 4 sinA.sinB.sinC.
One definition of sine and cosine is with a unitary circle. In this case, the sine is simply equal to the y-coordinate, and the cosine, the x-coordinate. Since the hypothenuse is 1, the equation in the question follows directly from Pythagoras' Law: x2 + y2 = r2, x2 + y2 = 1, cos2A + sin2A = 1. You can also derive it from the alternative definition of sine and cosine (ratios in a right triangle).
This is geometry/trigonometry, not calculus. That said, cos 2a = .3 The property you need: cos 2u = 1 - 2sin2u = 2cos2u - 1 Using the first equality: cos(2a) = 1 - 2sin2a Let u = a (.3) = 1 - 2sin2a Substitute cos(2a) = .3 .7 = sin2a Subtract .3 from both sides, get rid of negative sign sin a = .71/2 Square root both sides a = sin-1 .71/2= .991156 Not a special angle, use calculator.