Expand `|(sinx , 2),(3x , sinx)|`

Expand | (cosx, -sinx),(sinx , cosx)|

In the interval pi/2 lt x lt pi, find the value of x for which the matrix [(2sinx,3), (1 ,2sinx)]

The number of distinct real roots of the equation |{:(cosx, sinx, sinx), (sinx, cosx, sinx), (sinx, sinx, cosx):}|=0 in the interval [-\ pi/4,pi/4] is- a. 3 b. \ 4 c. \ 2 d. 1

If f(x)= =|{:(sinx+sin2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,sinx,1):}| then the value of int_(0)^(pi//2) f(x)dx , is

int (sinx-2/3+e^x) dx

If f(x) =|{:(sinx,cosx,sinx),(cosx,-sinx,cosx),(x,1,1):}| find the value of 2[f'(0)]+[f'(1)]^(2)

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

Prove that : (sinx-sin3x)/(sin^(2)x-cos^(2)x) = 2sinx

Find all the solution of 4 cos^(2)x sinx -2 sin^(2) x=3 sinx

The value of lim_(xrarr0) ((sinx)/(x))^((sinx)/(x-sinx)) , is