If sin (π - a) - cos (π + a) = 2 / 3 and a is the second quadrant angle, then sin (2 / π + a) + cosa (2 / π + a)=

If sin (π - a) - cos (π + a) = 2 / 3 and a is the second quadrant angle, then sin (2 / π + a) + cosa (2 / π + a)=


sin(π-a)-cos(π+a)
=sina+cosa=√2/3
Square on both sides
sin²a+cos²a+2sinacosa=2/9
1+2sinacosa=2/9
2sinacosa=-7/9
(sina-cosa)²
=sin²a+cos²a-2sinacosa
=1+7/9
=16/9
In the second quadrant, Sina > 0 > cosa
So Sina cosa = 4 / 3
Original formula = cosa Sina = - 4 / 3