Is ((4sin^2(x)))/(tan^2(x))=4cos^2(x) ?

The answer to whether ((4sin^2(x)))/(tan^2(x))=4cos^2(x) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove ((4sin^2(x)))/(tan^2(x))=4cos^2(x)

prove

\frac{( 4 sin ^{2} ( x ) )}{tan ^{2} ( x )} = 4 cos^{2} (x)

True

Solution steps

\frac{4 sin ^{2} ( x )}{tan ^{2} ( x )} = 4 cos^{2} (x)

Manipulating left side

\frac{4 sin ^{2} ( x )}{tan ^{2} ( x )}

Express with sin, cos

\frac{4 sin ^{2} ( x )}{tan ^{2} ( x )}

Use the basic trigonometric identity:

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

= \frac{4 sin ^{2} ( x )}{( \frac{s i n ( x )}{c o s ( x )} ) ^{2}}

Simplify

\frac{4 sin ^{2} ( x )}{( \frac{s i n ( x )}{c o s ( x )} ) ^{2}} : 4 cos^{2} (x)

\frac{4 sin ^{2} ( x )}{( \frac{s i n ( x )}{c o s ( x )} ) ^{2}}

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

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

Apply exponent rule:

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

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

= \frac{4 sin ^{2} ( x )}{\frac{s i n ^{2} ( x )}{c o s ^{2} ( x )}}

Apply the fraction rule:

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

= \frac{4 sin ^{2} ( x ) cos ^{2} ( x )}{sin ^{2} ( x )}

Cancel the common factor:

sin^{2} (x)

= 4 cos^{2} (x)

= 4 cos^{2} (x)

= 4 cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{tan ( 2 x ) + tan ( x )}{1 - tan ( 2 x ) tan ( x )} = tan (3 x)

csc (x) \cdot (sin (x) + tan (x)) = 1 + sec (x)

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

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

cos^{2} (θ) (1 + tan^{2} (θ)) = cos^{2} (x)

Is ((4sin^2(x)))/(tan^2(x))=4cos^2(x) ?
The answer to whether ((4sin^2(x)))/(tan^2(x))=4cos^2(x) is True