Is (sec(θ)cos(θ))/(cot(θ))=tan(θ) ?

The answer to whether (sec(θ)cos(θ))/(cot(θ))=tan(θ) is True

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prove (sec(θ)cos(θ))/(cot(θ))=tan(θ)

prove

\frac{sec ( θ ) cos ( θ )}{cot ( θ )} = tan (θ)

True

Solution steps

\frac{sec ( θ ) cos ( θ )}{cot ( θ )} = tan (θ)

Manipulating left side

\frac{sec ( θ ) cos ( θ )}{cot ( θ )}

Express with sin, cos

\frac{cos ( θ ) sec ( θ )}{cot ( θ )}

Use the basic trigonometric identity:

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

= \frac{cos ( θ ) \frac{1}{c o s ( θ )}}{cot ( θ )}

Use the basic trigonometric identity:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Multiply

cos (θ) \frac{1}{cos ( θ )} sin (θ) : sin (θ)

cos (θ) \frac{1}{cos ( θ )} sin (θ)

Multiply fractions:

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

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

Cancel the common factor:

cos (θ)

= 1 \cdot sin (θ)

Multiply:

1 \cdot sin (θ) = sin (θ)

= sin (θ)

= \frac{sin ( θ )}{cos ( θ )}

= \frac{sin ( θ )}{cos ( θ )}

= \frac{sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

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

= tan (θ)

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (θ - α) = 1

sin (x) (1 + cos (2 x)) = sin (2 x) cos (x)

(sec (x) - tan (x)) (1 + sin (x)) = cos (x)

tan (- x) = cos (x)

\frac{1}{cos ( x )} - cos (x) = tan (x) sin (x)

Is (sec(θ)cos(θ))/(cot(θ))=tan(θ) ?
The answer to whether (sec(θ)cos(θ))/(cot(θ))=tan(θ) is True