If `cos^(-1)x-cos^(-1)y/2=alpha,t h e n4x^2-4x ycosalpha+y^2` is equal to (a)4 (b) `2sin^2alpha` (c) `-4sin^2alpha` (d) `4sin^2alpha`

If sin^(-1)x+sin^(-1)y=pi/2,t h e n(1+x^4+y^4)/(x^2-x^2y^2+y^2) is equal to

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

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

If f(x)=x^(11)+x^9-x^7+x^3+1 and f(sin^(-1)(sin8)=alpha,alpha is constant, then f(tan^(-1)(t a n8) is equal to alpha (b) alpha-2 (c) alpha+2 (d) 2-alpha

x=sqrt(a^2cos^2alpha+b^2sin^2alpha)+sqrt(a^2sin^2alpha+b^2cos^2alpha) then x^2=a^2+b^2+2sqrt(p(a^2+b^2)-p^2) , where p is equal to (a) a^2cos^2alpha+ b^2sin^2alpha (b) a^2sin^2alpha+b^2cos^2alpha (c) (1/2)(a^2+b^2+(a^2-b^2)cos2alpha) (d) (1/2)(a^2+b^2-(a^2-b^2)cos2alpha)

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

If theta is eliminated from the equations x=a"cos"(theta-alpha) and y=bcos(theta-beta), then (x^2/a^2)+(y^2/b^2)-(2xy)/(ab)cos(alpha-beta) is equal to (a) sec^2(alpha-beta) (b) cos e c^2(alpha-beta) (c) cos^2(-beta) (d) sin^2(alpha-beta)

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