Is sin(x)=tan(x)cos(x) ?

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

prove sin(x)=tan(x)cos(x)

prove

sin (x) = tan (x) cos (x)

True

Solution steps

sin (x) = tan (x) cos (x)

Manipulating right 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

p ro v e tan (2 x) = 2 sin (x) cos (x) sec (2 x)

p ro v e tan (x) csc (x) = \frac{1}{cos ( x )}

p ro v e cos (18 0^{\circ} - θ) = - cos (θ)

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