Question

How do you prove `csc(t)cos(t)=cot(t)`?

Answer 1

See explanation

Explanation:

`csc` (cosecant) is the reciprocal of sine, so it is hypotenuse over opposite side to the angle

`cos` is adjacent side to the angle over hypotenuse

`cot` is the reciprocal of tangent, so it is adjacent side to angle over opposite side to angle

Let's use `H` to represent hypotenuse, `O` to represent opposite, and `A` to represent adjacent

`H/O*A/H=cancel(H)/O*A/cancel(H)=A/O rarr` `A/O` represents cotangent