`sin(pi/3-x)cos(pi/6+x)+cos(pi/3-x)sin(pi/6+x)=1`

Prove that. cos(pi/3)cos(pi/6)+sin(pi/3)sin(pi/6)=cos(pi/6)

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

(sin (pi + x) cos ((pi) / (2) + x) tan ((3 pi) / (2) -x) cot (2 pi-x)) / (sin (2 pi-x) cos (2 pi + x) csc (-x) sin ((3 pi) / (2) -x)) = 1

Prove that: sin ((8pi)/3) cos ((23pi)/6)+cos ((13pi)/3) sin ((35pi)/6)=1/2

Prove that sin (10pi)/(3) cos (13pi)/(6) + cos (8pi)/(3) sin (5pi)/(6) = -1

sin pi/3 = 2sin pi/6 cos pi/6

Prove that, sin((8pi)/(3))cos((23pi)/(6))+cos((13pi)/(3))sin((35pi)/(6))=(1)/(2)

If y="sec"(tan^(-1)x),t h e n (dy)/(dx) at x=1 is (a) cos(pi/4) (b) sin(pi/2) (c) sin(pi/6) (d) cos(pi/3)

sin(x-pi/6)+cos(x-pi/3)=sqrt3 sinx

If f(x)=sin^2x+sin^2(x+pi/3)+cos x.cos(x+pi/3) and g(5/4)=1 , then