Is 1/(sin(x)cos(x))=2csc(2x) ?

The answer to whether 1/(sin(x)cos(x))=2csc(2x) is True

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prove 1/(sin(x)cos(x))=2csc(2x)

prove

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

True

Solution steps

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

Manipulating right side

2 csc (2 x)

Express with sin, cos

2 csc (2 x)

Use the basic trigonometric identity:

csc (x) = \frac{1}{sin ( x )}

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

Simplify

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

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 2 = 2

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

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

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

Rewrite using trig identities

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

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

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

Divide the numbers:

\frac{2}{2} = 1

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

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

We showed that the two sides could take the same form

\Rightarrow True

Is 1/(sin(x)cos(x))=2csc(2x) ?
The answer to whether 1/(sin(x)cos(x))=2csc(2x) is True