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) 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

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

sin (a + b) + sin (a - b) = 2 sin (a) cos (b)

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

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

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