9514 1404 393
Explanation:
It is often useful to put everything in terms of sine and cosine.
sin(x)·(tan(x) +cot(x))
= sin(x)·(sin(x)/cos(x) + cos(x)/sin(x))
= sin(x)²/cos(x) +cos(x) . . . . . . use the distributive property*
= (sin(x)² +cos(x)²)/cos(x) . . . . . combine terms over a common denominator
= 1/cos(x)
= sec(x)
_____
* The expression inside parentheses could have been combined to ...
(sin(x)² +cos(x)²)/(sin(x)·cos(x))
Then the sin/sin factors cancel, leaving the expression on line 4.
