Is tan(4x)*cos(4x)=sin(4x) ?

The answer to whether tan(4x)*cos(4x)=sin(4x) is True

prove tan(4x)*cos(4x)=sin(4x)

prove

tan (4 x) \cdot cos (4 x) = sin (4 x)

True

Solution steps

tan (4 x) cos (4 x) = sin (4 x)

Manipulating left side

tan (4 x) cos (4 x)

Express with sin, cos

cos (4 x) tan (4 x)

Use the basic trigonometric identity:

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

= cos (4 x) \frac{sin ( 4 x )}{cos ( 4 x )}

Simplify

cos (4 x) \frac{sin ( 4 x )}{cos ( 4 x )} : sin (4 x)

cos (4 x) \frac{sin ( 4 x )}{cos ( 4 x )}

Multiply fractions:

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

= \frac{sin ( 4 x ) cos ( 4 x )}{cos ( 4 x )}

Cancel the common factor:

cos (4 x)

= sin (4 x)

= sin (4 x)

= sin (4 x)

We showed that the two sides could take the same form

\Rightarrow True

p ro v e tan (θ) = csc (θ) sec (θ) - cot (θ)

p ro v e sec (x) - sec (x) sin (x^{2}) = cos (x^{2})

p ro v e (1 + cot^{2} (x)) = \frac{1}{sin ^{2} ( x )}

p ro v e sin (x) (1 + csc (x)) = 1 + sin (x)

p ro v e (sec^{2} (θ) - 1) (sin^{2} (θ) - 1) = - sin^{2} (θ)

Is tan(4x)*cos(4x)=sin(4x) ?
The answer to whether tan(4x)*cos(4x)=sin(4x) is True