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

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

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

prove

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

True

Solution steps

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

Manipulating left side

cos (x) tan (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

\frac{sin ( 2 θ )}{sin ( θ )} - \frac{cos ( 2 θ )}{cos ( θ )} = sec (θ)

\frac{sec ( x )}{csc ( x )} + \frac{sin ( x )}{cos ( x )} = 2 tan (x)

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

sec (2 θ) = \frac{sec ^{2} ( θ )}{1 - tan ^{2} ( θ )}

cos (2 a) = cos^{2} (a) - sin^{2} (a)