If `f(x) = |{:( cos (2x) ,, cos ( 2x ) ,, sin ( 2x) ), ( - cos x,, cosx ,, - sin x ), ( sinx,, sin x,, cos x ):}|`, then

(1 + sin 2x + cos 2x )/( cos x + sin x ) = 2 cos x

(cos 4x sin 3x -cos 2x sin x )/(sin 4x sin x+ cos 6x cos x)= tan 2x

If f(x) = |{:(cos^(2)x, cosx.sinx, -sin x),(cos x sinx ,sin^(2)x ,cos x),(sinx , -cos x , 0):}| then for all x

If f(x) = |{:(cos^(2)x, cosx.sinx, -sin x),(cos x sinx ,sin^(2)x ,cos x),(sinx , -cos x , 0):}| then for all x

" Let f(x) " =|{:(cos x,,sin x,,cosx),( cos 2x,,sin 2x,,2cos 2x),(cos 3x,,sin 3x,,3cos 3x):}| then find the values of f' (pi//2) .

2tan2x = (cos x + sin x) / (cos x-sin x) - (cos x-sin x) / (cos x + sin x)

cosx + sinx = cos2x + sin2x

If f(x) = |(1+sin^(2)x,cos^(2)x,4 sin 2x),(sin^(2)x,1+cos^(2)x,4 sin 2x),(sin^(2)x,cos^(2)x,1+4 sin 2x)| What is the maximum value of f(x)?

If f(x)=|{:(cosx,sinx,cos x),(cos2x,sin2x,2cos2x),(cos3x,sin3x,3cos3x):}| find f^-1 (pi/2)

int (cos x - sin x)/(cosx + sinx) (2+2 sin 2x) dx =