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

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Answer 1 · 2018-04-10T23:21:56

See explanation

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

$cos$ $cos$ is adjacent side to the angle over hypotenuse

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

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

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

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