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

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

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

prove

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

True

Solution steps

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

Manipulating left side

sin (x) sec (x)

Express with sin, cos

sec (x) sin (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

Multiply:

1 \cdot sin (x) = sin (x)

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

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

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

Rewrite using trig identities

Use the basic trigonometric identity:

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

\frac{\frac{1}{c s c ( x )}}{cos ( x )}

Simplify

\frac{\frac{1}{c s c ( x )}}{cos ( x )}

Apply the fraction rule:

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

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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