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a) sin²a - 1 + cos²a + (1-sina)(a+sina) = (sin²a+ cos²a) - 1 + (1-sin²a) = 1 - 1 + 1 - sin²a = 1-sin²a = cos²a
b) (2sin²a-1)/(1-2cos²a) = -(1-2sin²a)/(1-2cos²a) = (1-2sin²a)/(2cos²a-1) = cos2a/cos2a = 1
c) (cos²a-1)/(3-3sin²a) = - (1-cos²a)/(3(1-sin²a)) = - sin²a/3cos²a = -1/3 * tg²a
d) 4/sin²a - 4ctg²a = 4/sin²a - 4cos²a/sin²a = (4-4cos²a)/sin²a = (4(1-cos²a))/sin²a = 4sin²a/sin²a = 4
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