Let `f(x)=|(cosx,sinx,cosx),(cos2x,sin2x,2cos2x),(cos3x,sin3x,3cos3x)|` Then `f'(pi/2)=`

If the determinant |(cos2x, sin^2x,cos4x),(sin^2x , cos2x,cos^2x),(cos4x,cos^2x,cos2x)| is expanded in powers of sinx , then the constant term in the expansion is :

Let f(x) =cos x sin 2x , then :

(cos 4x+cos3x+cos2x)/(sin 4x+sin3x+sin2x)=cot3x

(cos 4x+cos3x+cos2x)/(sin 4x+sin3x+sin2x)=cot3x

int e^(x)[(1+sinx cosx)/(cos^(2)x)]dx

If A=[(cosx,sinx),(-sinx,cosx)] , show that A^(2)=[(cos2x,sin2x),(-sin2x,cos2x)] and A^(1)A=1 .

int( sinx +5 cos x)/(3 sin x+2 cosx) dx

3(sinx-cosx)^(4)+6(sinx+cosx)^(2)+4(sin^(6)x+cos^(6)x)=

Let f(x)=|(cos x,e^(x^2) , 2x cos^2x/2),(x^2, sec x, sinx+x^3),(1,2,x+tan x)| then the value of int_(-pi/2)^(pi/2)(x^2+1)(f(x)+f''(x))dx

d/dx {(cosx + sinx)/(cos x - sin x)} =