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

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

Prove that (a) sin^(2)(pi/6) + cos^(2)( pi/3) - tan^(2)(pi/4) = -1/2 (b) sin((8pi)/3) cos((23pi)/6) + cos((13pi)/3) sin((35pi)/6) = 1/2

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

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

sin((13pi)/3)sin((8pi)/3)+cos((2pi)/3)sin((5pi)/6)=1/2

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

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

Prove that: sin((3pi)/8-5)cos( pi/8+5)+cos((3pi)/8-5)sin(pi/8+5)=1

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

Prove that: 2sin^2(pi/6)+cosec^2((7pi)/6)cos^2(pi/3)=3/2