Is sin(x)=(cos(x))/(cot(x)) ?

The answer to whether sin(x)=(cos(x))/(cot(x)) is True

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prove sin(x)=(cos(x))/(cot(x))

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Cancel the common factor:

cos (x)

= sin (x)

= sin (x)

= sin (x)

We showed that the two sides could take the same form

\Rightarrow True

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

tan (x) + cot (x) = cot (x) sec^{2} (x)

(1 + sin (z)) (1 - sin (z)) = \frac{1}{sec ^{2} ( z )}

\frac{tan ( x )}{sec ( x ) + 1} = csc (x) - cot (x)

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

Is sin(x)=(cos(x))/(cot(x)) ?
The answer to whether sin(x)=(cos(x))/(cot(x)) is True