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

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

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{2 sin ( x ) cos ( x ) sec ( x )}{2}

Express with sin, cos

\frac{2 cos ( x ) sec ( x ) sin ( x )}{2}

Use the basic trigonometric identity:

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

= \frac{2 cos ( x ) \frac{1}{c o s ( x )} sin ( x )}{2}

Simplify

\frac{2 cos ( x ) \frac{1}{c o s ( x )} sin ( x )}{2} : sin (x)

\frac{2 cos ( x ) \frac{1}{c o s ( x )} sin ( x )}{2}

Multiply

2 cos (x) \frac{1}{cos ( x )} sin (x) : 2 sin (x)

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

Multiply fractions:

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

= \frac{1 \cdot 2 cos ( x ) sin ( x )}{cos ( x )}

Cancel the common factor:

cos (x)

= 1 \cdot 2 sin (x)

Multiply the numbers:

1 \cdot 2 = 2

= 2 sin (x)

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

Divide the numbers:

\frac{2}{2} = 1

= sin (x)

= sin (x)

= sin (x)

We showed that the two sides could take the same form

\Rightarrow True

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