Is (2cos^2(x))/(sin(2x))= 1/(tan(x)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove (2cos^2(x))/(sin(2x))= 1/(tan(x))

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Double Angle identity:

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

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

Simplify

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

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

Divide the numbers:

\frac{2}{2} = 1

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

Cancel the common factor:

cos (x)

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

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

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

Manipulating right side

\frac{1}{tan ( x )}

Express with sin, cos

\frac{1}{tan ( x )}

Use the basic trigonometric identity:

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

= \frac{1}{\frac{s i n ( x )}{c o s ( x )}}

Simplify

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

\frac{1}{\frac{s i n ( x )}{c o s ( x )}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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