" (A) "f(x)=cos((pi)/(sqrt(3))sin x+sqrt((2)/(3))pi cos x)

In each of the following cases find the period of the function if it is periodic. (i) f(x)="sin"(pi x)/(sqrt(2))+"cos"(pi x)/(sqrt(3)) " (ii) " f(x)="sin"(pi x)/(sqrt(3))+"cos"(pi x)/(2sqrt(3))

In each of the following cases find the period of the function if it is periodic. (i) f(x)="sin"(pi x)/(sqrt(2))+"cos"(pi x)/(sqrt(3)) " (ii) " f(x)="sin"(pi x)/(sqrt(3))+"cos"(pi x)/(2sqrt(3))

In each of the following cases find the period of the function if it is periodic. (i) f(x)="sin"(pi x)/(sqrt(2))+"cos"(pi x)/(sqrt(3)) " (ii) " f(x)="sin"(pi x)/(sqrt(3))+"cos"(pi x)/(2sqrt(3))

In each of the following cases find the period of the function if it is periodic. (i) f(x)="sin"(pi x)/(sqrt(2))+"cos"(pi x)/(sqrt(3)) " (ii) " f(x)="sin"(pi x)/(sqrt(3))+"cos"(pi x)/(2sqrt(3))

Prove that : int_(0)^(pi//2) (sqrt(cos x))/(sqrt(sin x+ sqrt(cos x)))dx=(pi)/(4)

Prove that : int_(0)^(pi//2) (sqrt(cos x))/(sqrt(sin x+ sqrt(cos x)))dx=(pi)/(4)

Find the extreme values of the following function over R. (i) sin^(2) (60^(0) + x) + sin^(2) (60^(0) - x) (ii) cos (x+ (Pi)/(3) ) + 2sqrt(2) sin (x+ (pi)/(3))-3 (iii) 3 sin^(2) x+ 5 cos^(2) x (iv) cos 2 x+ cos^(2) x (v ) cos x cos ((2pi)/(3) + x) cos ((2pi)/(3)-x)

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

cos((3pi)/(4)+x)-cos ((3pi)/(4)-x)=-sqrt(2) sin x

If cos (pi/12) = (sqrt(2) + sqrt(6))/(4) , then all x in (0,pi/2) such that (sqrt(3)-1)/(sin x) + (sqrt(3)+1)/(cos x) = 4sqrt(2) , then find x.