Is (3sin^2(x))/(tan^2(x))=3cos^2(x) ?

The answer to whether (3sin^2(x))/(tan^2(x))=3cos^2(x) is True

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prove (3sin^2(x))/(tan^2(x))=3cos^2(x)

prove

\frac{3 sin ^{2} ( x )}{tan ^{2} ( x )} = 3 cos^{2} (x)

True

Solution steps

\frac{3 sin ^{2} ( x )}{tan ^{2} ( x )} = 3 cos^{2} (x)

Manipulating left side

\frac{3 sin ^{2} ( x )}{tan ^{2} ( x )}

Express with sin, cos

\frac{3 sin ^{2} ( x )}{tan ^{2} ( x )}

Use the basic trigonometric identity:

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

= \frac{3 sin ^{2} ( x )}{( \frac{s i n ( x )}{c o s ( x )} ) ^{2}}

Simplify

\frac{3 sin ^{2} ( x )}{( \frac{s i n ( x )}{c o s ( x )} ) ^{2}} : 3 cos^{2} (x)

\frac{3 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{3 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{3 sin ^{2} ( x ) cos ^{2} ( x )}{sin ^{2} ( x )}

Cancel the common factor:

sin^{2} (x)

= 3 cos^{2} (x)

= 3 cos^{2} (x)

= 3 cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{1 + sin ( - x )}{cos ( x ) tan ( x ) - 1} = - 1

sec (A) - \frac{cos ( A )}{1 + sin ( A )} = tan (A)

sin (3 a) = 3 sin (a) - sin (a)

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

Is (3sin^2(x))/(tan^2(x))=3cos^2(x) ?
The answer to whether (3sin^2(x))/(tan^2(x))=3cos^2(x) is True