If ` (sinx-cosx)= 0` then find `(sin^3 x- cos^3x)`

If sinx+cosx=a , then (i) sin^(6)x+cos^(6)x=..... (ii) abs(sinx-cosx)=.....

If 0lt=xlt=2pi, then the number of solutions of 3(sinx+cosx)-2(sin^3x+cos^3x)=8 is

Number of solution(s) of the equation (sinx)/(cos3x)+(sin3x)/(cos9x)+(sin9x)/(cos27x)=0 in the interval (0,pi/4) is____________

Evaluate : int_(0)^(pi/2)(sin^2x-cos^2x)/(sin^3x+cos^3x)dx

Evaluate: int(sin2x(1-3/2cosx))/e^(sin^2x+cos^3x)dx

Show that, sin3x + cos3x = (cosx-sinx)(1+4sinx cosx)

Find the number of solution of the equations sin^3 x cos x + sin^(2) x* cos^(2) x+sinx * cos^(3) x=1 , when x in[0,2pi]

Find the number of solution(s) of following equations: (i) x^(2)-sinx-cosx+2=0 (ii) sin^(2)x - 2sinx - x^(2)-3=0, x in [0,2pi]

Evaluate the following integrals. int (sinx + cos x)/((sin x - cos x)^(3))dx

If sinx+sin^2x+sin^3x=1 then find the value of cos^6x-4cos^4x+8cos^2x