Is (2cot(x))/(csc^2(x))=sin(2x) ?

The answer to whether (2cot(x))/(csc^2(x))=sin(2x) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove (2cot(x))/(csc^2(x))=sin(2x)

prove

\frac{2 cot ( x )}{csc ^{2} ( x )} = sin (2 x)

True

Solution steps

\frac{2 cot ( x )}{csc ^{2} ( x )} = sin (2 x)

Manipulating left side

\frac{2 cot ( x )}{csc ^{2} ( x )}

Express with sin, cos

= 2 cos (x) sin (x)

Rewrite using trig identities

= sin (2 x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{csc ^{2} ( x )}{1 + tan ^{2} ( x )} = cot^{2} (x)

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

\frac{1}{2 cot ( x ) ( 1 - cos ^{2} ( x ) )} = csc (2 x)

cos^{4} (x) - sin^{4} (x) = 2 cos^{2} (x) - 1

tan (x) (cot (x) + tan (x)) = sec^{2} (x)

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