`tan(pi/4+alpha)=(1+sin2alpha)/(cos2alpha)`

The value of expression (tan alpha+sin alpha)/(2"cos"^(2)(alpha)/(2)) for alpha=(pi)/(4) is :

The value of expression (tan alpha+sin alpha)/(2"cos"^(2)(alpha)/(2)) for alpha=(pi)/(4) is :

Givent that (pi)/(2)

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 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) .

Prove that, (cos alpha + sin alpha)/(cos alpha -sin alpha)-(cos alpha - sin alpha)/(cos alpha + sin alpha) = 2 tan 2 alpha

Evaluate tan^(-1)((3sin 2alpha)/(5+3cos2alpha)) +tan^(-1)((1)/(4)tan alpha) , where, -(pi)/(2) lt alpha lt (pi)/(2) .

Prove the identity,cos((3 pi)/(2)+4 alpha)+sin(3 pi-8 alpha)-sin(4 pi-12 alpha)=4cos2 alpha cos4 alpha sin6 alpha

Prove that sin4 alpha=4tan alpha (1- tan^(2)alpha)/((1+tan^2 alpha)^2

Prove that, (sin alpha + cos alpha)/(cos alpha-sin alpha)=tan2 alpha + sec 2 alpha