Prove that: `cos18^0-sin 18^0=sqrt(2)sin27^0`

If cos theta + sin theta = sqrt(2) cos theta , show that cos theta - sin theta = sqrt(2) sin theta .

Show that : cos 38 ^@ cos 52 ^@ - sin 38^@ sin 52 ^@ = 0

If sin A + sin^(2)A + sin^(3)A =1 , then , prove that cos^(6) A - 4 cos^(4) A + 8 cos^(2) A =4 .

Solve 2cos^(2)x+3 sin x=0

Solve the equation sin x + cos x -2sqrt2 sin x cos x =0

Show that cos 36^(@) cos 54 ^(@) -sin 36^(@) sin 54^(@) =0

Number of integral solution of the equation log_(sin x) sqrt(sin^(2)x)+ log_(cos x)sqrt( cos^(2)x)= , where x in [0,6pi] is

Prove that: (sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = (2)/(sin^(2)A-cos^(2)A)=(2)/(2sin^(2)A-1)=(2)/(1-2 cos^(2)A) .

Prove that : (a) (sintheta+costheta)^(2)=1+2sin thetacostheta (b)Sin A cos A tan A+cos A sin A cot A=1

Solve the following equation: \ 3cos^2theta-2\ sqrt(3)sinthetacostheta-3sin^2theta=0