Question

For which value of theta is cot theta equal to cos theta?

A) pi
B) 2 pi
C) pi/2
D) 0

Answer 1

`(cos \theta)/(sin \theta)= cos \theta`

If we multiply by cross we got:

`cos \theta = sin \theta cos \theta`

We can divide both sides of the last equation by
`cos \theta` and we got:

`sin \theta = 1`

And if we apply arcsin in both sides we got:

`\theta = arcsin (1) = (\pi)/(2)`

And the best solution would be:

C) pi/2

Explanation:

For this case we want to solve the following equation:

`cot \theta = cos \theta`

And we know that by definition
`cot \theta = (cos \theta)/(\sin \theta)`

And replacing we got:

`(cos \theta)/(sin \theta)= cos \theta`

If we multiply by cross we got:

`cos \theta = sin \theta cos \theta`

We can divide both sides of the last equation by
`cos \theta` and we got:

`sin \theta = 1`

And if we apply arcsin in both sides we got:

`\theta = arcsin (1) = (\pi)/(2)`

And the best solution would be:

C) pi/2