" (1) "tan^(-1)(x sin alpha)/(1-x cos alpha)

Differentiate tan^(-1) ((x sin alpha)/(1-x cos alpha))

If tan alpha = (x sin beta)/(1-x cos beta) " and " tan beta = (y sin alpha)/(1-y cos alpha),"show that", (sin alpha)/(sin beta) = x/y .

Prove that for real x, (tan(x+alpha))/(tan(x-alpha)) where alpha ne pi/4, 3pi/4 cannot lies between (1- sin2 alpha)/(1+ sin 2alpha) and (1+ sin2 alpha)/(1- sin 2alpha) .

If alpha in (-(3pi)/2,-pi) , then the value of tan^(-1)(cot alpha)-cot^(-1)(tan alpha)+sin^(-1)(sin alpha)+cos^(-1)(cos alpha) is equal to

If cos y=x cos(alpha-y) then (1+x^(2)-2x cos alpha)*(dy)/(dx) is (A) sin alpha (B) -sin alpha (C) cos alpha (D) -cos alpha

If an angle alpha is divided into two parts A&B such that A-B=x and tan A:tan B=k:1 Then the value of sin x is (A) (k+1)/(k-1)sin alpha (k)/(k+1)sin alpha (C) (k-1)/(k+1)sin alpha (D) tan alpha

(1+sin alpha)/(1+cos alpha)*(1+sec alpha)/(1+cos ec alpha)=tan alpha

Prove the following Identity: (tan alpha+sec alpha-1)/(tan alpha-sec alpha+1)=(1+sin alpha)/(cos alpha)

If" " tan theta = (sin alpha - cos alpha)/(sin alpha + cos alpha),"prove that",2 cos^(2) theta = 1 + sin 2 alpha.

IF tan alpha = ( sin alpha - cos alpha )/( sin alpha + cos alpha) , then sin alpha + cos alpha is