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Simplify fully: $\sin{(90^{\circ}-x)}.\cos{(180^{\circ}+x)} + \tan{x}.\cos{x}.\sin{(x-180^{\circ})}$
in Mathematics by Diamond (75,934 points)
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apply reduction formula and complement angles of sin and cos

$= \cos{x}.(-\cos{x})+ \dfrac{\sin{x}}{\cos{x}} . \cos{x}.(-\sin{x})$

$= -\cos^2{x} - \sin^2{x}$ , then use square identity

$= -1$
by Diamond (43,720 points)
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