Is (2cos(x))/(cos^2(x))=2sec(x) ?

The answer to whether (2cos(x))/(cos^2(x))=2sec(x) is True

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prove (2cos(x))/(cos^2(x))=2sec(x)

prove

\frac{2 cos ( x )}{cos ^{2} ( x )} = 2 sec (x)

True

Solution steps

\frac{2 cos ( x )}{cos ^{2} ( x )} = 2 sec (x)

Manipulating left side

\frac{2 cos ( x )}{cos ^{2} ( x )}

Simplify

= \frac{2}{cos ( x )}

Rewrite using trig identities

Use the basic trigonometric identity:

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

\frac{2}{\frac{1}{s e c ( x )}}

Simplify

\frac{2}{\frac{1}{s e c ( x )}}

Apply the fraction rule:

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

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

Apply rule

\frac{a}{1} = a

= 2 sec (x)

2 sec (x)

2 sec (x)

We showed that the two sides could take the same form

\Rightarrow True

Is (2cos(x))/(cos^2(x))=2sec(x) ?
The answer to whether (2cos(x))/(cos^2(x))=2sec(x) is True