Please simplify the following problem Simplify the following

Please simplify the following problem.

Simplify the following expression. sin(pi + x) + tan x cos(x - pi/2) sin(pi + x) + tan x cos (x - pi/2) =

sin (pi + x) = -sin x [Since, pi+x means third quadrant. And sin is negative in 3rd quadrant]

cos (x - pi/2) = cos (- (x-pi/2)) = cos( pi/2 - x) = sin x [Since pi/2 -x means 1st quadrant. ]

So,

sin(pi+x) + tan x cos (x - pi/2) = (-sinx) + (tan x)(sin x)

= -sinx + sin²x/cosx

= (-sin x cos x + sin²x)/cosx

= sinx (sin x - cos x) / cos x

= tan x ( sin x - cos x)