Is ((sin^2(t)))/(tan^2(t))=cos^2(t) ?

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

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prove ((sin^2(t)))/(tan^2(t))=cos^2(t)

prove

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

True

Solution steps

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

Manipulating left side

\frac{sin ^{2} ( t )}{tan ^{2} ( t )}

Express with sin, cos

\frac{sin ^{2} ( t )}{tan ^{2} ( t )}

Use the basic trigonometric identity:

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

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

Simplify

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

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

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

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

Apply exponent rule:

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

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

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

Apply the fraction rule:

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

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

Cancel the common factor:

sin^{2} (t)

= cos^{2} (t)

= cos^{2} (t)

= cos^{2} (t)

We showed that the two sides could take the same form

\Rightarrow True

sin (A) sec (A) = tan (A)

csc (x) tan (x) cos (x) = 1

tan^{2} (\frac{x}{2}) + 2 tan (\frac{x}{2}) - 5 = 3 tan (\frac{x}{2})

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

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

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