cos x + sinx tan COS I-sin I

If y = tan^(-1){(cos x + sinx)/(cos x - sin x)} " then " (dy)/(dx) = ?

Let y=tan ^(-1)((1-cos x)/(sin x)) i) Express 1-cos x and sinx in terms of sin (x/2) and cos (x/2) ii) Hence find (dy/dx) .

Simplifty : tan^-1[(a cos x - b sin x)/(b cos x + a sinx)] if a/b tan x > -1

IF alpha , beta and gamma are angles such that tan alpha + tan beta + tan gamma = tan alpha tan beta tan gamma and x= cos alpha + i sin alpha , y = cos beta + i sin beta and z= cos gamma + i sin gamma , then xyz =

Prove that: (i) (1+"sin" 2theta-cos 2theta)/(1+"sin" 2theta+cos 2theta)="tan" theta . (ii) 2 tan 2x=(cos x+"sin" x)/(cos x-"sin" x)-(cos x-"sin" x)/(cos x+"sin" x) .

Prove that : 2 tan 2x= (cos x+sinx)/(cos x-sinx)-(cos x- sinx)/(cos x+sinx) .

If f (x) = tan ^(-1) ((cos x- sinx)/(cos x+ sin x)) then the value of (d)/(dx) f(x) is-

If f(x) = (cos x + i sin x)(cos 3x + i sin 3x) ….(cos (2n - 1)x + i(sin(2n - 1)x) , then f^(11)(x) is

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