tan(90+x)=tan(x-50)tan(x)tan(x+50) wht is the min value of ''x''?

tan (90+x)/tan x = tan( x+50). tan (x-50)/1

using componendo and dividendo priciple , we have

(tan (90+x) + tan x) /( tan (90+x) - tan x )= (tan( x+50). tan (x-50) + 1) / (tan( x+50). tan (x-50) - 1)

Sin (90+2x) / sin 90 = cos 100 / cos 2x

here sin 90 = 1

so, by multiplying 2 on both sides we have

2 sin(2x+90).cos 2x + 2 cos 100 = 0

sin (4x+100) + 1+ 2cos 100 =0

on simplification gives

cos 4x + 1 - 2.sin 10 = 0

2* cos²2x = 2* sin 10

so, cos²2x = sin 10

so , x = cos^-1[(sin 10)^1/2] / 2