Solve the equation cosx tanx 0 lessthanorequalto x lessthan

Solve the equation cos(x) = tan(x) 0 lessthanorequalto x lessthanorequalto pi/2.

Solution

cos x=tan x

cos x = tan x ............( As tan x = sin x / cos x )
cos x = sin x / cos x
cos x * cos x = sin x
cos² x = sin x ............( As cos² x = 1 - sin²x )
1 - sin²x = sin x
1 = sin x + sin² x
0 = sin² x + sin x - 1
Let sin x = A
0 = A² + A - 1
A² + A - 1 = 0
I used quadratic equation formula and i found
A = 0.618034 ...OR... A = -1.618034
As A = sin x
So
sin x = 0.618034 ...........OR........... sin x = -1.618034
x = sin^-1 (0.618034).......OR........... x = sin^-1 (-1.618034)
x = 38.17° .....................OR............ x = Nil ( no solution )
So...
x = 38.17°