[" f "sin A=(1)/(2),cos B=(sqrt(3))/(2)," where "(pi)/(2)

sin A=(1)/(2),cos B=(sqrt(3))/(2), where (pi)/(2)

Prove that (i) "sin " (7pi)/(12) " cos " (pi)/(2) - "cos " *(7pi)/(12) " sin " (pi)/(4) = (sqrt(3))/(2) (ii) " sin " (pi)/(4) " cos " (pi)/(2) + "cos"(pi)/(4) " sin " (pi)/(12) = (sqrt(3))/(2) (iii) " cos " (2pi)/(3) " cos " (pi)/(4) - " sin " (2pi)/(3) " sin " (pi)/(4) =(-(sqrt(3) +1))/(2sqrt(2))

sin(A+B)=1/sqrt(2) cos(A-B)=sqrt3|2

Prove that (i) " sin " .(pi)/(6). " cos " .(pi)/(6) = (sqrt(3))/(4) " " (iii) cos^(2) .(pi)/(2) - sin^(2) .(pi)/(2) =(sqrt(3))/(2)

let a and b be real numbers such that sin a+sin b=(1)/(sqrt(2)) and cos+cos b=sqrt((3)/(2)) then

If sin (3A-B) = 1 and cos (2A - B) = (sqrt(3))/(2) , then the value of sin A and cos B are .

Find sin 2x if cos x=sqrt3/2 where 0 le x le pi/2

If f(x) is continuous at x=(pi)/(4) where f(x)=(2sqrt(2)-(cos x+sin x)^(3))/(1-sin2x) ,for x!=(pi)/(4) then f((pi)/(4))=

If z_(1) = sqrt(2)(cos""(pi)/(4) + "" i sin""(pi)/(4)) and z_(2) = sqrt(3)(cos""(pi)/(3) + i sin""(pi)/(3)) , then |z_(1)z_(2)| is

Prove that (i) "cos " ((pi)/(3) +x) =(1)/(2) ( " cos " x - sqrt(3) sin x) (ii) " sin " ((pi)/(4) + x) + " sin " ((pi)/(4)-x) =sqrt(2) " cos " x (iii) (1)/(sqrt(2)) " cos ((pi)/(4) + x) = (1)/(2) " (cos x - sin x) " (iv) " cos x + cos " ((2pi)/(3) +x) + " cos " ((2pi)/(3)-x) =0