Is tan^4(x)=((sin^4(x)))/(cos^4(x)) ?

The answer to whether tan^4(x)=((sin^4(x)))/(cos^4(x)) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove tan^4(x)=((sin^4(x)))/(cos^4(x))

prove

tan^{4} (x) = \frac{( sin ^{4} ( x ) )}{cos ^{4} ( x )}

True

Solution steps

tan^{4} (x) = \frac{sin ^{4} ( x )}{cos ^{4} ( x )}

Manipulating left side

tan^{4} (x)

Express with sin, cos

tan^{4} (x)

Use the basic trigonometric identity:

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

= (\frac{sin ( x )}{cos ( x )})^{4}

Simplify

(\frac{sin ( x )}{cos ( x )})^{4} : \frac{sin ^{4} ( x )}{cos ^{4} ( x )}

(\frac{sin ( x )}{cos ( x )})^{4}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{sin ^{4} ( x )}{cos ^{4} ( x )}

= \frac{sin ^{4} ( x )}{cos ^{4} ( x )}

= \frac{sin ^{4} ( x )}{cos ^{4} ( x )}

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (π) = 1 - cos^{2} (π)

tan (π + x) = tan (x)

\frac{( cot ( x ) + tan ( x ) )}{cot ( x ) - tan ( x )} = sec (2 x)

cot (a) + tan (a) = sec (a) csc (a)

tan (x) + cot (x) = sec (x) + csc (x)

Is tan^4(x)=((sin^4(x)))/(cos^4(x)) ?
The answer to whether tan^4(x)=((sin^4(x)))/(cos^4(x)) is True