Is (cos(2x)-cos(4x))/(sin(2x)sin(4x))=tan(x) ?

The answer to whether (cos(2x)-cos(4x))/(sin(2x)sin(4x))=tan(x) is False

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prove (cos(2x)-cos(4x))/(sin(2x)sin(4x))=tan(x)

prove

\frac{cos ( 2 x ) - cos ( 4 x )}{sin ( 2 x ) sin ( 4 x )} = tan (x)

False

Solution steps

\frac{cos ( 2 x ) - cos ( 4 x )}{sin ( 2 x ) sin ( 4 x )} = tan (x)

Show that the two sides are not equal

For

\frac{cos ( 2 x ) - cos ( 4 x )}{sin ( 2 x ) sin ( 4 x )} = tan (x)

plug in

x = 1

\frac{cos ( 2 \cdot 1 ) - cos ( 4 \cdot 1 )}{sin ( 2 \cdot 1 ) sin ( 4 \cdot 1 )} = - 0.34511 \dots

\frac{cos ( 2 \cdot 1 ) - cos ( 4 \cdot 1 )}{sin ( 2 \cdot 1 ) sin ( 4 \cdot 1 )}

Refine to a decimal form

= - 0.34511 \dots

tan (1) = 1.55740 \dots

tan (1)

Refine to a decimal form

= 1.55740 \dots

The two sides are not equal

\Rightarrow False

\frac{tan ( x ) + cot ( x )}{csc ( x )} = sec (x)

\frac{csc ( x )}{cot ( x )} = sec (x)

sin (2 t) - tan (t) = tan (t) cos (2 t)

tan (- x) = - tan (x)

csc^{2} (x) (1 - cos^{2} (x)) = 1

Is (cos(2x)-cos(4x))/(sin(2x)sin(4x))=tan(x) ?
The answer to whether (cos(2x)-cos(4x))/(sin(2x)sin(4x))=tan(x) is False