Is 1/(cos(θ))=(tan(θ))/(sin(θ)) ?

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

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prove 1/(cos(θ))=(tan(θ))/(sin(θ))

prove

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

True

Solution steps

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

Manipulating right side

\frac{tan ( θ )}{sin ( θ )}

Express with sin, cos

\frac{tan ( θ )}{sin ( θ )}

Use the basic trigonometric identity:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Cancel the common factor:

sin (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

sin (x) \cdot tan (x) = sec (x) - cos (x)

(tan (y) + cot (y)) sin (y) cos (y) = 1

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

sin (x) \cdot cot (x) = cos (x)

(csc (θ) - cot (θ)) (csc (θ) + cot (θ)) = 1

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