Question

Упростить:

1+ctg(3p/2+a)sina * cosa - cos^2a

Answer 1

$1 + ctg( \frac{3\pi}{2} + \alpha ) \times sin \alpha \times cos \alpha - {(cos \alpha )}^{2} = \\ = 1 - tg \alpha \times sin \alpha \times cos \alpha - {(cos \alpha )}^{2} = \\ = 1 - \frac{sin \alpha }{cos \alpha } \times sin \alpha \times cos \alpha - {(cos \alpha )}^{2} = \\ = 1 - {(sin \alpha )}^{2} - {(cos \alpha )}^{2} = 1 - ( {(sin \alpha )}^{2} + {(cos \alpha )}^{2}) = \\ = 1 - 1 = 0$



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