Question

How to prove `cos(theta-pi/2)=sin(theta)` is false?

Answer 1

`cos(theta - pi/2) = sin(theta)` is true

Explanation:

By the difference of angles formula for `cos(alpha - beta)` we find:

`cos(theta - pi/2) = cos(theta) cos(pi/2) + sin(theta) sin(pi/2)`

`color(white)(cos(theta - pi/2)) = cos(theta)(0) + sin(theta)(1)`

`color(white)(cos(theta - pi/2)) = sin(theta)`