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

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

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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

sin (θ) \cdot (cot (θ) + tan (θ)) = sec (θ)

tan (x) + 10 = \frac{sin ( x ) + 10}{cos ( x )}

\frac{( sin ^{2} ( t ) )}{tan ^{2} ( t )} = cos^{2} (t)

sin (A) sec (A) = tan (A)

csc (x) tan (x) cos (x) = 1