Question

Verify the identity. (1 point) cot x minus pi divided by two. = -tan x

Answer 1

Apply the definitions:

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

which implies

`\cot\left(x-(\pi)/(2)\right) = (\cos\left(x-(\pi)/(2)\right))/(\sin\left(x-(\pi)/(2)\right))`

We also have the identities

`\cos\left(x-(\pi)/(2)\right) = -\sin(x)`

`\sin\left(x-(\pi)/(2)\right) = \cos(x)`

Which means

`\cot\left(x-(\pi)/(2)\right) = (\cos\left(x-(\pi)/(2)\right))/(\sin\left(x-(\pi)/(2)\right)) = (-\sin(x))/(\cos(x)) = -\tan(x)`