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

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Answer 1 · 2016-01-26T03:40:48

$csc x$

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....

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