# Express all six functions of θ in terms of tan θ.

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### 1 Answer

The functions sin θ, cos θ, sec θ, cosec θ and cot θ have to be expressed in terms of tan θ.

Use the identity `(sec theta)^2 = 1 + (tan theta)^2`

=> `sec theta = sqrt(1 + (tan theta)^2)`

`cos theta = 1/(sqrt(1+(tan theta)^2))`

`cot theta = 1/tan theta`

Using `(sin theta)^2 = 1 - (cos theta)^2`

=> `(sin theta)^2 = 1 - 1/(1+(tan theta)^2)`

=> `(sin theta)^2 = (tan theta)^2/(1 +(tan theta)^2)`

=> `sin theta = (tan theta)/(sqrt(1+(tan theta)^2))`

`cosec theta = sqrt(1+(tan theta)^2)/tan theta`