Is (sin(x)sec(x))/(tan(x))=1 ?

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

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prove (sin(x)sec(x))/(tan(x))=1

prove

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

True

Solution steps

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

Manipulating left side

\frac{sin ( x ) sec ( x )}{tan ( x )}

Express with sin, cos

\frac{sec ( x ) sin ( x )}{tan ( x )}

Use the basic trigonometric identity:

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

= \frac{\frac{1}{c o s ( x )} sin ( x )}{tan ( x )}

Use the basic trigonometric identity:

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

= \frac{\frac{1}{c o s ( x )} sin ( x )}{\frac{s i n ( x )}{c o s ( x )}}

\frac{\frac{1}{c o s ( x )} sin ( x )}{\frac{s i n ( x )}{c o s ( x )}} = 1

\frac{\frac{1}{c o s ( x )} sin ( x )}{\frac{s i n ( x )}{c o s ( x )}}

Apply the fraction rule:

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

= \frac{\frac{1}{c o s ( x )} sin ( x ) cos ( x )}{sin ( x )}

Multiply

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos (x)

= 1 \cdot sin (x)

Multiply:

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

= sin (x)

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

Apply rule

\frac{a}{a} = 1

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

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