Is tan(x)csc(x)= 1/(cos(x)) ?

The answer to whether tan(x)csc(x)= 1/(cos(x)) is True

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prove tan(x)csc(x)= 1/(cos(x))

prove

tan (x) csc (x) = \frac{1}{cos ( x )}

True

Solution steps

tan (x) csc (x) = \frac{1}{cos ( x )}

Manipulating left side

tan (x) csc (x)

Express with sin, cos

csc (x) tan (x)

Use the basic trigonometric identity:

csc (x) = \frac{1}{sin ( x )}

= \frac{1}{sin ( x )} tan (x)

Use the basic trigonometric identity:

tan (x) = \frac{sin ( x )}{cos ( x )}

= \frac{1}{sin ( x )} \cdot \frac{sin ( x )}{cos ( x )}

Simplify

\frac{1}{sin ( x )} \cdot \frac{sin ( x )}{cos ( x )} : \frac{1}{cos ( x )}

\frac{1}{sin ( x )} \cdot \frac{sin ( x )}{cos ( x )}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot sin ( x )}{sin ( x ) cos ( x )}

Cancel the common factor:

sin (x)

= \frac{1}{cos ( x )}

= \frac{1}{cos ( x )}

= \frac{1}{cos ( x )}

We showed that the two sides could take the same form

\Rightarrow True

Is tan(x)csc(x)= 1/(cos(x)) ?
The answer to whether tan(x)csc(x)= 1/(cos(x)) is True