Step by step solution to "Establish identity sec⁡θcsc⁡θ+sin⁡θcos⁡θ=2tan⁡θ"

coexpennan

Answered question

2021-09-10

Establish identity

\frac{\sec θ}{\csc θ} + \frac{\sin θ}{\cos θ} = 2 \tan θ

Jaylen Fountain

Skilled2021-09-11Added 169 answers

Given identity

\frac{\sec θ}{\csc θ} + \frac{\sin θ}{\cos θ} = 2 \tan θ

First from the left-hand side,

\frac{\sec θ}{\csc θ} + \frac{\sin θ}{\cos θ}

Here use the trigonometry reciprocal identity,

\sec θ = \frac{1}{\cos θ}

and

\csc θ = \frac{1}{\sin θ}

\frac{\sec θ}{\csc θ} + \frac{\sin θ}{\cos θ} = \frac{\frac{1}{\cos θ}}{\frac{1}{\sin θ}} + \frac{\sin θ}{\cos θ}

= \frac{\sin θ}{\cos θ} + \frac{\sin θ}{\cos θ}

= 2 \tan θ

Therefore it is established that the left-hand side equal to the right-hand side quantity.

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?