Simplify to an expression involving a single trigonometric f

Simplify to an expression involving a single trigonometric function with no fractions. cos(- x) + sin(- x)/cot(- x)

Solution

cos(-x) +sin(-x)/cot(-x)

we use the trigonemteric angle properties:

sin(-x) = -sinx ; cos(-x) = cosx ; cot(-x) = -cotx

So, cos(-x) +sin(-x)/cot(-x) = cosx + -sinx/-cotx

= cosx +sinx/cotx

= cosx + sinx*tanx

= cosx+ sin^2x/cosx

= (cos^2x +sin^2x)/cosx

= 1/cosx

= secx