If `tan(pi/4+)=tan^3(pi/4+x/2)dot` Prove that `(siny)/(sinx)=(3+sin^2x)/(1+3sin^2x)` .

If tan((pi)/(4)+(y)/(2))=tan^(3)((pi)/(4)+(x)/(2))* Prove that (sin y)/(sin x)=(3+sin^(2)x)/(1+3sin^(2)x)

Prove that (1- sin 2x)/(1+ sin 2x) = tan^(2) .((pi)/(4)-x)

if tan ((pi)/(4)+(y)/(2))=tan^(3)((pi)/(4)+(x)/(2)) then (3+sin^(2)x)/(1+3sin^(2)x)=

If tan(cot x)=cot(tan x), prove that :sin2x=(4)/((2n+1)pi)

Prove that tan^(-1)((cosx)/(1+sinx))=(pi/4-x/2)

If tan^(3) (alpha/2+ pi/4) = tan(beta/2 +pi/4) then prove that sin beta = ((3 + sin^(2)alpja) sin alpha) /(1 + 3sin^(2)alpha)

tan x+tan(x+(pi)/(3))+tan(x+2(pi)/(3))=3 prove that (3tan x-tan^(3)x)/(1-3tan^(2)x)=1

If tan x+tan(x+(pi)/(3))+tan(x+(2 pi)/(3))=3 then prove that (3tan x-tan^(3)x)/(1-3tan^(2)x)=1

If tan((pi)/(4)+(theta)/(2))=tan^(3)((pi)/(4)+(alpha)/(2)) then sin(theta)=(sin(alpha)(3+sin^(2)(alpha)))/(1+3sin^(2)(alpha))

Prove that 2sin x+tan x>=3xquad (0<=x<(pi)/(2))