`4(sin2 4^0+cos6^0)=sqrt(3)+sqrt(15)`

Prove that : sin 75^0 = (sqrt(6) + sqrt(2))/4

Show that: sin 50^0cos85^0=(1-sqrt(2)sin35^0)/(2sqrt(2))

Show that: sin 50^0cos95^0=(sqrt(2)sin35^0-1)/(2sqrt(2))

The number of values of x in (0, pi) satisfying the equation (sqrt(3) "sin" x + "cos" x) ^(sqrt(sqrt(3)"sin" 2x -"cos" 2x+ 2)) = 4 , is

Prove that: cos18^0=(sqrt(10+2sqrt(5)))/4 .

lim_(x to 0) (sin^(2) x)/(sqrt(2)-sqrt(1+cos x))= (A) sqrt(2) (B) 2 (C) 4 (D) 4sqrt(2)

Prove that: (cos30^0+sin60^0)/(1+cos60^0+sin30^0)=(sqrt(3))/2

The sum of all the solution(s) of the equation sin^(-1)2x=cos^(-1)x is 0 (2) 2/(sqrt(5)) (3) 1/(sqrt(5)) (4) (-1)/(sqrt(5))

The value of the expression ((sin3theta)/(sintheta))^2-((cos3theta)/(costheta))^2,w h e ntheta=(7. 5)^0, is a. 4(sqrt(3)+1) b. (sqrt(3)-1) c. 2(sqrt(6)+sqrt(2)) d. 8/(sqrt(6)-sqrt(2))

The value of sin^(-1){cot(sin^(-1)(sqrt((2-sqrt3)/4)+cos^(-1)(sqrt(12)/4)+sec^(-1)sqrt2)} is