The expression `3[sin^4(3/2pi-alpha)+sin^4(3pi+alpha)]-2[sin^6(1/2pi+alpha)+sin^6(5pi-alpha)]` is equal to

sin 3 alpha = 4 sin alpha sin(x + alpha) sin(x-alpha)

If alpha in (-(3pi)/2,-pi) , then the value of tan^(-1)(cotalpha)-cot^(-1)(tanalpha)+sin^(-1)(sinalpha)+cos^(-1)(cosalpha) is equal to (a) 2pi+alpha (b) pi+alpha (c) 0 (d) pi-alpha

If cosbeta is the geometric mean between sinalphaa n dcosalpha, where 0ltalpha,betaltpi/ 2, then cos2beta is equal to(a) -2sin^2(pi/ 4-alpha) (b) -2cos^2(pi/ 4+alpha) (c) -2sin^2(pi/4+alpha) (d) 2cos^2(pi/ 4-alpha)

IF sin ^(16) alpha = 1/5 then the value of (1) /(cos ^2 alpha) +(1)/( 1 + sin ^2 alpha) +(2)/(1+ sin ^4 alpha) + ( 4 )/( 1+ sin ^8 alpha) is equal to

if cos alpha + sin alpha = 3/4 , then sin ^6 alpha + cos ^6 alpha =

Prove that sin^2alpha-sin^4alpha= cos^2alpha-cos^4alpha

If sin alpha + cos alpha = b, then sin 2 alpha is equal to

The value of (sin(pi-alpha))/(sin alpha-cos alpha tan.(alpha)/(2))-cos alpha is