cos(α+β)+2sinαsinβ=cosαcosβ−sinαsinβ+2sinαsinβ=
cosαcosβ+sinαsinβ=cos(α−β)
если \alpha -\beta=\piα−β=π , то cos(\alpha -\beta ) =cos\pi =-1.cos(α−β)=cosπ=−1.
б)
\frac{sin^{2}\alpha +sin(\pi-\alpha)cos (\frac{\pi }{2} -\alpha) }{tq(\pi+\alpha)ctq( \frac{3\pi }{2} -\alpha ) } = \frac{sin^{2}\alpha +sin\alpha*sin\alpha }{tq\alpha*tq\alpha } =\frac{2sin^{2} \alpha }{tq^{2} \alpha } =\frac{2sin^{2}\alpha }{\frac{sin^{2} \alpha }{cos^{2} \alpha } } =2cos^{2} \alpha .
tq(π+α)ctq(
2
3π
−α)
sin
2
α+sin(π−α)cos(
2
π
−α)
=
tqα∗tqα
sin
2
α+sinα∗sinα
=
tq
2
α
2sin
2
α
=
cos
2
α
sin
2
α
2sin
2
α
=2cos
2
α.
в)
cos7xcos6x+sin7xsin6x=cos(7x-6x)=cosx.cos7xcos6x+sin7xsin6x=cos(7x−6x)=cosx.
а)2 11/24:0,75=59/24:75/100=59/24: 3/4=59/24×4/3=236/72=59/18=3 5/18
б)3 5/18-1 11/30=59/18-41/30=295/90-123/90=172/90=86/45=1 41/45
2)
а)4 1/3:13=13/3×1/13=13/39
б)20:1 1/4=20/1:5/4=20/1×4/5=80/5=16
в) 0,125×40=125/100×40=5/4×40/1=200/4=50
г) 13/39+16+50=66 13/39
3)
а) 1,2×0,5=12/10×5/10=60/20=3
б) 3: 4/5=3/1×5/4=15/4=3 3/4
в) 6 53/56-2,375=389/56-2375/1000=389/56- 19/8=389/56-133/56=256/56=32/7=4 4/7
г) 4 4/7+3 3/4=32/7+15/4=128/28+105/28=233/28=8 9/28