Is 1/(sec(x))+1=(sec(x)+1)/(sec(x)) ?

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

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prove 1/(sec(x))+1=(sec(x)+1)/(sec(x))

prove

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

True

Solution steps

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

Manipulating left side

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

Simplify

1 + \frac{1}{sec ( x )} : \frac{sec ( x ) + 1}{sec ( x )}

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

Convert element to fraction:

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

= \frac{1 \cdot sec ( x )}{sec ( x )} + \frac{1}{sec ( x )}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot sec ( x ) + 1}{sec ( x )}

Multiply:

1 \cdot sec (x) = sec (x)

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

tan^{2} (θ) = sec (θ) csc (θ) tan (θ) - 1

sin (x + y) = cos (\frac{π}{2} - (x + y))

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

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

csc (s) - sin (s) = cos (s) cot (s)

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