Is sin(θ)=cos(θ)tan(θ) ?

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

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prove sin(θ)=cos(θ)tan(θ)

prove

sin (θ) = cos (θ) tan (θ)

True

Solution steps

sin (θ) = cos (θ) tan (θ)

Manipulating right side

cos (θ) tan (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

sin (\frac{π}{2} + θ) = cos (θ)

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

cos (α + β) = cos (α) cos (β) - sin (α) sin (β)

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

\frac{sin ( θ )}{tan ( θ )} = cos (θ)