" 11."(i)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

Find the modulus of the following complex numbers i) 1+i tan alpha ii) tan alpha-i iii) 1-sin alpha+i cos 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 beta = (n sin alpha cos alpha)/(1-n sin^(2) alpha), "show that", tan (alpha - beta) = (1 - n) tan alpha.

If cos^(-1)[(cos alpha+ cos beta)/(1+cos alpha cos beta)]=2 Tan^(-1)x then x=