Is 2/(cot(x)tan(x))=sin(2x) ?

The answer to whether 2/(cot(x)tan(x))=sin(2x) is False

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove 2/(cot(x)tan(x))=sin(2x)

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

\frac{2}{cot ( 1 ) tan ( 1 )} = 2

\frac{2}{cot ( 1 ) tan ( 1 )}

Rewrite using trig identities:

cot (1) = \frac{1}{tan ( 1 )}

cot (1)

Use the basic trigonometric identity:

cot (x) = \frac{1}{tan ( x )}

= \frac{1}{tan ( 1 )}

= \frac{2}{\frac{1}{t a n ( 1 )} tan ( 1 )}

\frac{2}{\frac{1}{t a n ( 1 )} tan ( 1 )} = 2

\frac{2}{\frac{1}{t a n ( 1 )} tan ( 1 )}

Multiply

\frac{1}{tan ( 1 )} tan (1) : 1

\frac{1}{tan ( 1 )} tan (1)

Multiply fractions:

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

= \frac{1 \cdot tan ( 1 )}{tan ( 1 )}

Cancel the common factor:

tan (1)

= 1

= \frac{2}{1}

Apply rule

\frac{a}{1} = a

= 2

= 2

sin (2 \cdot 1) = 0.90929 \dots

sin (2 \cdot 1)

Refine to a decimal form

= 0.90929 \dots

The two sides are not equal

\Rightarrow False

Is 2/(cot(x)tan(x))=sin(2x) ?
The answer to whether 2/(cot(x)tan(x))=sin(2x) is False