Question

How do you simplify `sin x + cot x cos x`?

Answer 1

`csc x`

Explanation:

We start from the given

`sin x+cotx cos x`

`sin x+(cos x/sin x)*cos x`

`sin x*(sin x/sin x)+(cos x cos x)/sin x`

because `sin x/sin x=1`, we can always use it in any part of the equation or expression.

fractions having the same denominator can be combined.

it follows

`sin ^2 x/sin x+cos ^2 x/sin x`

`(sin^2 x+cos^2 x)/sin x`

but `sin^2 x+cos^2 x=1`

therefore

`1/sin x`

simplifies to

`csc x`

Have a nice day !!! from the Philippines....