Prove that sin(x)+sin(x)cot^2(x)=csc(x)

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll factor sin x and we'll get:

`sin x*(1 + cot^2 x) = csc x`

From Pythagorean identity, we'll get:

`1 + cot^2 x = 1/(sin^2 x)`

We'll re-write the expression:

`sinx*(1/(sin^2 x)) = csc x`

We'll simplify and we'll get:

`1/sin x = csc x`

Since the result represents a basic identity, then the given expression represents an identity, too.