Is 1/(cos(x)sin(x))=csc(x)sec(x) ?

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

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prove 1/(cos(x)sin(x))=csc(x)sec(x)

prove

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

True

Solution steps

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

Manipulating right side

csc (x) sec (x)

Express with sin, cos

csc (x) sec (x)

Use the basic trigonometric identity:

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

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 1 = 1

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

tan (2 x) - sin (2 x) = tan (2 x) sin (2 x)

tan^{2} (x) + sec^{2} (x) = 1

sec (x) tan (x) - sin (x) = sin (x) tan^{2} (x)

\frac{1 - cos ( 2 x )}{csc ( x )} = 2 sin^{3} (x)

(1 + sin (x))^{2} + cos^{2} (x) = 2 (1 + sin (x))

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