How do you simplify $(cot θ + tan θ) sec θ$ ?

Question

5747 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-23T03:52:22

Recall that $tantheta = sintheta/costheta$ .

Since $cottheta =1/tantheta$ , cottheta = 1/(sintheta/costheta)= costheta/sintheta#.

Also, $sectheta = 1/costheta$ .

$=(sintheta/costheta + costheta/sintheta)1/costheta$

$=((sin^2theta + cos^2theta)/(costhetasintheta))1/costheta$

Recall the Pythagorean Identity $sin^2theta + cos^2theta = 1$ :

$=1/(costhetasintheta costheta)$

$=1/(cos^2thetasintheta)$

Use the rearranged form of the Pythagorean identity presented above.

$=1/((1 - sin^2theta)sintheta)$

$=1/(sintheta - sin^3theta$

We could have also finished with $sec^2thetacsctheta$ , because $1/sintheta = csctheta$ and $1/costheta = sectheta$

Hopefully this helps!

How do you simplify (cot θ + tan θ) sec θ(cot θ + tan θ) sec θ?