Prove that `3(sinx-cosx)^4+4(sin^6x+cos^6x)+6(sinx+cosx)^2=13`

Integrate the function int (4 cos x-3 sin x)/((8 sin x + 6 cos x)^(2))dx.

Find the derivatives of: sin^3x+cos^6x

Prove that (Delta^2/E)x^3=6x

Prove that cot^(-1) ((sqrt(1+sin x) +sqrt(1-sin x))/(sqrt(1+sin x) -sqrt(1-sinx)))=(x)/(2), x in (0, (pi)/(4)) .

Solve : sin^2x-5sinxcosx-6cos^2x=0

Evaluate the integrals int(sinx + cosx)/(sqrt(1+sin2x) dx

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

Evaluate the integrals int(1+3sinx)/(cos^2x) dx

Prove the following sin^6theta+cos^6theta=1-3sin^2thetacos^2theta