How do you prove cot(θ)sec(θ)=csc(θ)?

1 Answer
Burglar
May 30, 2016

Applying the definition of cot,sec,csc and tan.

Explanation:

Recall the definition of these functions:

cot(θ)=1tan(θ)
sec(θ)=1cos(θ)
csc(θ)=1sin(θ)

Then we want to prove

cot(θ)sec(θ)=csc(θ)

that is equivalent to

1tan(θ)1cos(θ)=1sin(θ)

We recall that tan(θ)=sin(θ)cos(θ), consequently
1tan(θ)=cos(θ)sin(θ).
I substitute in the previous equation

1tan(θ)1cos(θ)=1sin(θ)

cos(θ)sin(θ)1cos(θ)=1sin(θ)

1sin(θ)=1sin(θ).

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