How do you simplify $csc x(sin x + cos x)$ ?

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Answer 1 · 2016-02-12T11:50:12

$1 + cot x$

Knowing the two identities

$csc x = 1 / sin x " "$ and $" "cot x = cos x / sin x$ ,

you can simplify as follows:

$csc x (sin x + cos x ) = 1/ sin x (sin x + cos x)$

$= sin x / sin x + cos x / sin x$

$= 1 + cos x / sin x$

$= 1 + cot x$

How do you simplify csc x(sin x + cos x)csc x(sin x + cos x)?