Is tan(x)*cos(x)=sin(x) ?

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

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prove tan(x)*cos(x)=sin(x)

prove

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

True

Solution steps

tan (x) cos (x) = sin (x)

Manipulating left side

tan (x) cos (x)

Express with sin, cos

cos (x) tan (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos (x)

= sin (x)

= sin (x)

= sin (x)

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (x) csc^{2} (x) = csc^{2} (x) - 1

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

\frac{sec ( x ) + tan ( x )}{csc ( x ) + 1} = tan (x)

tan (a) = \frac{sec ( a )}{csc ( a )}

sec (x) tan (x) cos (x) cot (x) = 1