Simplify
`[(3 sin 2 alpha)/(5 + 3 cos 2 alpha)] + tan^(-1) [(tan alpha)/(4)], " where " -(pi)/(2) lt alpha lt (pi)/(2)`

Simplify tan^(-1) [(3 sin 2 alpha)/(5 + 3 cos 2 alpha)] + tan^(-1) [(tan alpha)/(4)], " where " -(pi)/(2) lt alpha lt (pi)/(2)

Simplifytan^(-1) [(3 sin 2 alpha)/(5 + 3 cos 2 alpha)] + tan^(-1) [(tan alpha)/(4)], " where " -(pi)/(2) lt alpha lt (pi)/(2)

Simplify tan^-1[(3 sin 2alpha)/(5+3 cos2 alpha)]+tan^(-1)[(tan alpha)/4]

Simplify [(3sin2 alpha)/(5+3cos2 alpha)]+tan^(-1)[(tan alpha)/(4)], where -(pi)/(2)

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

Simplify [(3sin2alpha)/(5+3cos2alpha)]+tan^(-1)[(tanalpha)/4],w h e r e-pi/2

The expression (1 + sin 2 alpha )/( cos (2 alpha - 2pi) tan (alpha - (3pi)/(4 ))) -1/4 sin 2 alpha [ cot "" (alpha )/(2) + (alpha )/(2))] when simplified reduces to

Simplify: (cos(2pi + alpha)"cosec" (pi - alpha) tan (pi/2 + alpha))/("sec" (pi/2 + alpha) sin ((3pi)/2 - alpha) cot (2pi - alpha))

If sin alpha = (-3)/(5), where pi lt alpha lt (3pi)/(2), then cos ((alpha)/(2))=

If sin (alpha + beta) = 4/5 , cos (alpha - beta) = (12)/(13) 0 lt alpha lt (pi)/(4), 0 lt beta lt (pi)/(4), find tan 2 alpha .