Is 1/(cos(x))=(tan(x))/(sin(x)) ?

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

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prove 1/(cos(x))=(tan(x))/(sin(x))

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Cancel the common factor:

sin (x)

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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tan^{4} (x) - sec^{4} (x) = 1 - 2 sec^{2} (x)

3 sin^{2} (x) - 9 sin (x) cot (x) + 7 cos^{2} (x) - 4 cos (x) = (4 cos (x) - 1) (cos (x) - 3)

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