Is (sin(2x)+sin(4x))/(cos(2x)+cos(4x))=tan(3x) ?

The answer to whether (sin(2x)+sin(4x))/(cos(2x)+cos(4x))=tan(3x) is True

Popular >

prove (sin(2x)+sin(4x))/(cos(2x)+cos(4x))=tan(3x)

prove

\frac{sin ( 2 x ) + sin ( 4 x )}{cos ( 2 x ) + cos ( 4 x )} = tan (3 x)

True

Solution steps

\frac{sin ( 2 x ) + sin ( 4 x )}{cos ( 2 x ) + cos ( 4 x )} = tan (3 x)

Manipulating left side

\frac{sin ( 2 x ) + sin ( 4 x )}{cos ( 2 x ) + cos ( 4 x )}

Rewrite using trig identities

= \frac{sin ( 3 x )}{cos ( 3 x )}

Use the basic trigonometric identity:

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

= tan (3 x)

We showed that the two sides could take the same form

\Rightarrow True

sec (A) csc (A) = cos (A) tan (A)

\frac{1}{tan ( b )} + tan (b) = \frac{sec ^{2} ( b )}{tan ( b )}

cos^{2} (x) - sin^{2} (x) = tan^{2} (x) sin^{2} (x)

sin (2 a) = 2 sin (a)

cos^{3} (x) = (cos (x))^{3}

Is (sin(2x)+sin(4x))/(cos(2x)+cos(4x))=tan(3x) ?
The answer to whether (sin(2x)+sin(4x))/(cos(2x)+cos(4x))=tan(3x) is True