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) 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

\frac{sin ( x + \frac{π}{2} )}{sin ( π - x )} = cot (x)

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

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

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

\frac{cot ^{2} ( t )}{csc ( t )} = csc (t) - sin (t)