`cot2x = cosx + sinx`

If f(x) = \begin{vmatrix} cos2x & cos2x & sin2x \\ -cosx & cosx & -sinx\\ sinx & sinx & cosx \end{vmatrix} then

"If "y=(sinx)^(cosx)+(cosx)^(sinx)", prove that "(dy)/(dx)=(sinx)^(cosx).[cot x cos x-sin x(log sinx)]+(cosx)^(sinx).[cosx(log cos x)-sinx tanx].

The value of 3(sinx - cosx)^4 + 6(sinx + cosx)^2 + 4 (sin^6 x + cos^6 x) is

Prove that (cosx + cosy)/(sinx - siny) = cot ((x-y)/2)

Find intcos2x*log((cosx+sinx)/(cosx-sinx))dx

Find intcos2x*log((cosx+sinx)/(cosx-sinx))dx

The number of distinct roots of |(sinx, cosx, cosx),(cosx, sinx, cosx),(cosx,cosx,sinx)|=0 in the interval -pi/4 le x le pi/4 is (A) 0 (B) 2 (C) 1 (4) 2

((sinx - x cosx)/(x sinx + cos x ))

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