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

1 Answer

Answer:

#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....