Is tan(θ)*cos(θ)=sin(θ) ?

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

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prove tan(θ)*cos(θ)=sin(θ)

prove

tan (θ) \cdot cos (θ) = sin (θ)

True

Solution steps

tan (θ) cos (θ) = sin (θ)

Manipulating left side

tan (θ) cos (θ)

Express with sin, cos

cos (θ) tan (θ)

Use the basic trigonometric identity:

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

= cos (θ) \frac{sin ( θ )}{cos ( θ )}

Simplify

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

cos (θ) \frac{sin ( θ )}{cos ( θ )}

Multiply fractions:

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

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

Cancel the common factor:

cos (θ)

= sin (θ)

= sin (θ)

= sin (θ)

We showed that the two sides could take the same form

\Rightarrow True

csc (x) + cot (x) = \frac{1 + cos ( x )}{sin ( x )}

\frac{cos ( x )}{1 - sin ( x )} = tan (\frac{x}{2} - \frac{π}{4})

(sin (x))^{2} = sin^{2} (x)

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

cot (x - y) = \frac{cot ( x ) cot ( y ) + 1}{cot ( y ) - cot ( x )}