Simplify the following trigonometric expression to the best of your abilities. sin (𝜃 + 𝜋 2 ) /cot(𝜃)

Answer 1

So if I’m reading the question correctly, that’s sin(theta+2pi) and since all of the trigonometric ratios start over every 2pi, it’s the same as saying sin(theta)/cot(theta).

Since cot(theta)=cos(theta)/sin(theta), what you have is sin(theta)/cos(theta)/sin(theta). When you divide by a fraction, you multiply by its reciprocal so you end up with sin(theta)*sin(theta)/cos(theta) which simplifies to sin^2(theta)/cos(theta).

Let me know if this helps.