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2012-09-29T21:55:14+04:00
2012-09-29T22:30:14+04:00

1. sin α = √(1-(cosα)^2)= √(1-16/25)= √(9/25)=3/5

 

tg  α = sin α/cos α=3/5*(-5/4)=-3/4

 

cos 2α = (cos α)^2 - (sin α)^2 = 16/25 - 9/25 = 7/25

 

 

2. cos 135 = -cos 45 = -√2/2

 

sin (8π/3) = 2*sin (4π/3)*cos(4π/3) = 2*sin 240*cos 240 = 2*sin 60*cos 60 = 2* √3/2*1/2 =  √3/2

 

tg (7π/3) = tg 240 = tg 60 = √3  

 

(cos  π/8)^2 - (sin  π/8)^2 = cos (2* π/8) = cos ( π/4) = cos 45 =  √2/2   

 

 

3. 1) = sin α*cos β - sin β*cos α +  sin β*cos α =  sin α*cos β

 

2) = (cos (π-α) + cos (π/2-α))* (cos (π-α) - cos (π/2-α)) = (-cos α + sin  α)*(-cos  α - sin α) =  (cos α - sin  α)*(cos  α + sin α) = (cos α)^2 - (sin  α)^2 = cos 2α

 

3)  = sin α*sin β + cos  α*cos β -  sin α*sin β =  cos α*cos β = cos (α-β)