if `2tanx=3tany` , show that `tan(x-y)=(sin2y)/(5-cos2y)`

If tanx=2/3 and tany=3/4 then tan(x+y)=

prove that: (sin2x-sin2y)/(cos2y-cos2x)=cot(x+y)

Prove that tan(x+y)=(tanx+tany)/(1-tanxtany)

(dy)/(dx)=(sin2y)/(x+tany)

(tanx)^(y)=(tany)^(x)

If cot theta = cos (x+y) "and" cot phi = cos (x-y), "show that" tan (theta- phi)=(2sin x sin y )/(cos^(2) x + cos^(2) y)

If (tan x) / (tan y) = (1 + cos ^ (2) x) / (1 + sin ^ (2) x), show that sin (3x + y) = 7sin (xy)

If (tan x) / (tan y) = (1 + cos ^ (2) x) / (1 + sin ^ (2) x), show that sin (3x + y) = 7sin (xy)

If tan x = tan y cos2 alpha prove that: tan (yx) = (tan ^ (2) alpha * sin2y) / (1 + tan ^ (2) alpha * cos2y)

If y=x+tanx , show that cos^(2)x(d^(2)y)/(dx^(2))-2y+2x=0 .