Is (sin(θ)sec(θ))/(tan(θ))=1 ?

The answer to whether (sin(θ)sec(θ))/(tan(θ))=1 is True

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prove (sin(θ)sec(θ))/(tan(θ))=1

prove

\frac{sin ( θ ) sec ( θ )}{tan ( θ )} = 1

True

Solution steps

\frac{sin ( θ ) sec ( θ )}{tan ( θ )} = 1

Manipulating left side

\frac{sin ( θ ) sec ( θ )}{tan ( θ )}

Express with sin, cos

\frac{sec ( θ ) sin ( θ )}{tan ( θ )}

Use the basic trigonometric identity:

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

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

Use the basic trigonometric identity:

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

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

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

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

Apply the fraction rule:

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

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

Multiply

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

\frac{1}{cos ( θ )} sin (θ) cos (θ)

Multiply fractions:

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

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

Apply rule

\frac{a}{a} = 1

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

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

tan (\frac{π}{6}) = \frac{1}{3}

cos (4 a) = 1 - 8 sin^{2} (a) cos^{2} (a)

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

cos (2 0^{\circ}) = cos (θ) + cos (θ)

Is (sin(θ)sec(θ))/(tan(θ))=1 ?
The answer to whether (sin(θ)sec(θ))/(tan(θ))=1 is True