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

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

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

prove

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

True

Solution steps

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

Manipulating left side

tan^{3} (x)

Express with sin, cos

tan^{3} (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Apply exponent rule:

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

cos (4 θ) = 1 - 8 sin^{2} (θ) cos^{2} (θ)

tan^{2} (x) - sin^{2} (x) = (tan (x) sin (x))^{2}

cos^{6} (10 5^{\circ}) = (\frac{1 + cos ( 21 0 ^{\circ} )}{2})^{3}

cos^{2} (θ) = sin^{2} (θ) - 1

\frac{tan ( 2 θ ) + cot ( 2 θ )}{sec ( 2 θ )} = csc (2 θ)

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