Is sin^2(x)sec(x)=(sin(x))/(cot(x)) ?

The answer to whether sin^2(x)sec(x)=(sin(x))/(cot(x)) is True

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prove sin^2(x)sec(x)=(sin(x))/(cot(x))

prove

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

True

Solution steps

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

Manipulating right side

\frac{sin ( x )}{cot ( x )}

Express with sin, cos

\frac{sin ( x )}{cot ( x )}

Use the basic trigonometric identity:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

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

sin (x) sin (x)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

sin (x) sin (x) = sin^{1 + 1} (x)

= sin^{1 + 1} (x)

Add the numbers:

1 + 1 = 2

= sin^{2} (x)

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

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

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

Rewrite using trig identities

Use the basic trigonometric identity:

cos (x) = \frac{1}{sec ( x )}

\frac{sin ^{2} ( x )}{\frac{1}{s e c ( x )}}

Simplify

\frac{sin ^{2} ( x )}{\frac{1}{s e c ( x )}}

Apply the fraction rule:

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

= \frac{sin ^{2} ( x ) sec ( x )}{1}

Apply rule

\frac{a}{1} = a

= sin^{2} (x) sec (x)

sin^{2} (x) sec (x)

sin^{2} (x) sec (x)

We showed that the two sides could take the same form

\Rightarrow True

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