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) 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

cos^{2} (y) - sin^{2} (y) = 1 - 2 sin^{2} (y)

cos (x) - cos^{3} (x) = cos (x) sin^{2} (x)

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

sin (x + y) - sin (x - y) = 2 cos (x) sin (y)

csc^{2} (θ) tan^{2} (θ) - 1 = tan^{2} (θ)