Given that cos β = 2 / 3, the terminal edge of angle a - β is on the nonnegative half axis of y-axis, the value of COS (2a-3 β) can be obtained

Given that cos β = 2 / 3, the terminal edge of angle a - β is on the nonnegative half axis of y-axis, the value of COS (2a-3 β) can be obtained

It's the Y-positive semiaxis
So cos (a - β) = 1
sin(a-β)=0
cos(2a-2β)=2cos²(a-β)-1=1
sin(2a-2β)=0
The original formula = cos ((2a-2 β - β)
=cos(2a-2β)cosβ+sin(2a-2β)sinβ
=2/3

It is known that there is a point m (- 3,4) on the terminal edge of angle A. if there is a point Q (sin2a, cos (2a + π / 3)), try to determine the quadrant of Q

cosa=x/r= -3/5
sina=y/r=4/5
Let Q (x, y)
x=sin2a=2sinacosa= -24/250
{x0
Q is in the second quadrant;

Given the terminal crossing point P (2a, - 3a) (a < 0) of angle α, the value of 2Sin α + cos α is obtained

x=2a,y=-3a
So r = √ (X & sup2; + Y & sup2;) = | a | 13
a

If α, β ∈ (3, π 4, π), sin (α + β) = - 35, sin (β - π 4) = 1213, then cos (α + π 4) = ()
A. 1665B. 5665C. -5665D. -1665

Then cos (α + π 4) = cos [(α + β) - (β - π 4)] = cos (α +...) = cos [(α + β) - (β - π 4)] = cos (α +...) = cos (α + π 4) = - 513