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

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

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

prove

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

True

Solution steps

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

Manipulating left 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

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

2 sin^{2} (x) + cos^{2} (x) = 1 + sin^{2} (x)

\frac{1}{cos ^{2} ( x ) 2 tan ( x )} = csc (2 x)

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

tan (y) - \frac{sec ^{2} ( y )}{tan ( y )} = - cot (y)

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