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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Cancel the common factor:

sin (x)

= sin (x) cos (x)

= sin (x) cos (x)

= cos (x) sin (x)

= sin (x) cos (x)

We showed that the two sides could take the same form

\Rightarrow True

cot^{4} (x) + 2 cot^{2} (x) + 1 = csc^{4} (x)

sin^{2} (β) + tan^{2} (β) + 1 = \frac{2}{cos ^{2} ( β )}

cot (x) - 1 = csc (x) (cos (x) - sin (x))

sec (A) csc (A) = 1

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

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