Is 2sec(β)=2*1/(cos(β)) ?

The answer to whether 2sec(β)=2*1/(cos(β)) is True

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prove 2sec(β)=2*1/(cos(β))

prove

2 sec (β) = 2 \cdot \frac{1}{cos ( β )}

True

Solution steps

2 sec (β) = 2 \cdot \frac{1}{cos ( β )}

Manipulating right side

2 \frac{1}{cos ( β )}

Simplify

= \frac{2}{cos ( β )}

Rewrite using trig identities

Use the basic trigonometric identity:

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

\frac{2}{\frac{1}{s e c ( β )}}

Simplify

\frac{2}{\frac{1}{s e c ( β )}}

Apply the fraction rule:

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

= \frac{2 sec ( β )}{1}

Apply rule

\frac{a}{1} = a

= 2 sec (β)

2 sec (β)

2 sec (β)

We showed that the two sides could take the same form

\Rightarrow True

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