Question

How do you verify this trig identity?

Answer 1

Explanation:

\frac{ \sin(x) \csc(x) }{ \cot(x) }

cot(x)

sin(x)csc(x)

Rewrite csc(x) in terms of sin

\frac{ \sin(x) \frac{1}{ \sin(x) } }{ \cot(x) }

cot(x)

sin(x)

sin(x)

1

Multiply the numerator. Notice that the factors in the numerator are reciprocal so they will factor out to 1.

\frac{1}{ \cot(x) }

cot(x)

1

Notice that cotangent and tan are reciprocal so

\tan(x) = \tan(x)tan(x)=tan(x)

Answer 2

Explanation:

`( \sin(x) \csc(x) )/( \cot(x) )`

Rewrite csc(x) in terms of sin

`( \sin(x) (1)/( \sin(x) ) )/( \cot(x) )`

Multiply the numerator. Notice that the factors in the numerator are reciprocal so they will factor out to 1.

`(1)/( \cot(x) )`

Notice that cotangent and tan are reciprocal so

`\tan(x) = \tan(x)`