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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply

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

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

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

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

Use the basic trigonometric identity:

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

= cot (x)

We showed that the two sides could take the same form

\Rightarrow True

3 + sin^{2} (x) = 4 - cos^{2} (x)

sin^{4} (m) - cos^{4} (m) = 1 - 2 cos^{2} (m)

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

tan (13 5^{\circ} + a) = \frac{tan ( a ) - 1}{tan ( a ) + 1}

tan (\frac{x}{2}) = \frac{tan ( x )}{( sec ( x ) + 1 )}

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