Is 1/(sin(θ)cot(θ))= 1/(cos(θ)) ?

The answer to whether 1/(sin(θ)cot(θ))= 1/(cos(θ)) is True

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prove 1/(sin(θ)cot(θ))= 1/(cos(θ))

prove

\frac{1}{sin ( θ ) cot ( θ )} = \frac{1}{cos ( θ )}

True

Solution steps

\frac{1}{sin ( θ ) cot ( θ )} = \frac{1}{cos ( θ )}

Manipulating left side

\frac{1}{sin ( θ ) cot ( θ )}

Express with sin, cos

\frac{1}{cot ( θ ) sin ( θ )}

Use the basic trigonometric identity:

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

= \frac{1}{\frac{c o s ( θ )}{s i n ( θ )} sin ( θ )}

Simplify

\frac{1}{\frac{c o s ( θ )}{s i n ( θ )} sin ( θ )} : \frac{1}{cos ( θ )}

\frac{1}{\frac{c o s ( θ )}{s i n ( θ )} sin ( θ )}

Multiply

\frac{cos ( θ )}{sin ( θ )} sin (θ) : cos (θ)

\frac{cos ( θ )}{sin ( θ )} sin (θ)

Multiply fractions:

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

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

Cancel the common factor:

sin (θ)

= cos (θ)

= \frac{1}{cos ( θ )}

= \frac{1}{cos ( θ )}

= \frac{1}{cos ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

tan^{8} (x) = tan^{6} (x) sec^{2} (x) - tan^{6} (x)

2 (sin (2 y) cos (2 y)) = sin (4 y)

csc^{2} (θ) \cdot (sin^{2} (θ)) = 1

tan (b) cos (b) + cot (b) cos (b) = csc (b)

1 + cot^{2} (z) = csc^{2} (z)

Is 1/(sin(θ)cot(θ))= 1/(cos(θ)) ?
The answer to whether 1/(sin(θ)cot(θ))= 1/(cos(θ)) is True