Express as a single Thgonometric function fx p sin px sinp

Express as a single Thgonometric function f(x, p) = sin (p+x) - sin(p + x)/cos (p + x) + cos (p - x)

Solution

f(x , p) = [ sin(x +p) - sin( p-x) ]/[ cos(p+x) +cos(p-x)]

use the sin(a+b) , sin(a -b) , cos(a+b) , cos(a-b) formulas.

= [ sinxcosp +cosxsinp - (sinpcosx -sinxcosp)]/[ cospcosx - sinxsinp+cospcosx+ sinpsinx]

= [2sinxcosp]/[2cospcosx]

=sinx/cosx

= tanx