Simplify and write thce trigonometric expression in terms of

Simplify and write thce trigonometric expression in terms of sine and cosine: tan x + cot x = 1/f(x) f(x) =

Solution

tanx +cotx = 1/f(x)

sinx/cosx +cosx/sinx = 1/f(x)

(sinx*sinx+ cosx*cosx)/sinxcosx = 1/f(x)

(sin^2x+cos^2x)/sinxcosx   = 1/f(x)

2/2sinxcosx = 1/f(x)

2/sin2x = 1/f(x)

f(x) = sin2x/2