(sin(- x) * cot x)/(sin(pi/2 - x))

Question

Simplify and evaluate where possible

Answer 1

When simplifying trig. functions, I follow 2 goal to make the process easier (not that these goal will always be achievable):

1. Rewrite trig. functions in terms of sine and cosine. Utilize identities to do so.
2. Rewrite the quantities inside each trig. function to be the same to create like terms. Utilize identities or analyze graphs to do so.

The purpose of this is to allow for the combination and/or canceling of them. For example, sin(x) + sin(2x) cannot be added together as they are not like terms, even though they are both sine.

Original problem: (sin(-x) * cot(x)) / sin(Π/2 - x)

sin(-x) = -sin(x)

cot(x) = cos(x) / sin(x)

sin(Π/2 - x) = cos(x)

(above determined by looking up identities reference sheet)

Problem after substitution: -sin(x) * (cos(x) / sin(x)) / cos(x)

sin(x) cancel/divide each other, and cos(x) cancel/divide each other. Which leave a -1.

Answer = -1

Answer 2

sin(-x)·cotx/sin(π/2 - x) = - ·sinx·cotx/cosx = - tanx·cotx = - 1