Establish the identity: <mstyle displaystyle="true" scriptlevel="0"> co

Avah Knapp

Avah Knapp

Answered question

2022-05-21

Establish the identity:
cot θ + sec θ cos θ + tan θ = sec θ cot θ

Answer & Explanation

Leah Conley

Leah Conley

Beginner2022-05-22Added 12 answers

Hint:
cot θ + sec θ = 1 tan θ + 1 cos θ = cos θ + tan θ tan θ cos θ
Anahi Jensen

Anahi Jensen

Beginner2022-05-23Added 4 answers

On the one hand
cot θ + sec θ cos θ + tan θ = cos θ sin θ + 1 cos θ cos θ + sin θ cos θ = cos 2 θ + sin θ sin θ cos θ ÷ cos 2 θ + sin θ cos θ = cos 2 θ + sin θ sin θ cos θ cos θ cos 2 θ + sin θ = 1 sin θ .
On the other,
sec θ cot θ = 1 cos θ cos θ sin θ = 1 sin θ .
Thus we have shown that
cot θ + sec θ cos θ + tan θ = sec θ cot θ

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?