Question

2. упростите выражение:

а) (cos^2 x-sin^2x-1)
_____________
(sinx+cosx)^2-1

б) 1-cos2x+sin2x
___________
cosx+sinx

Answer 1

a) $\frac{cos^{2}x-sin^{2}x-1}{(sinx+cosx)^{2}-1}= \frac{1-2*sin^{2}x-1}{sin^{2}x+2*sinx*cosx+cos^{2}x-1}= \frac{-2*sin^{2}x}{2*sinx*cosx}= \frac{-2sinx}{2cosx}= -tg(x)$
б) $\frac{1-cos2x+sin2x}{cosx+sinx}= \frac{1-(1-2*sin^{2}x+2*sinx*cosx)}{cosx+sinx} = \frac{2*sin^{2}x+2*sinx*cosx}{cosx+sinx}= 2sinx$