Question

Verify the identity by transforming the left-hand side into the right: sin 2x+sin 4x divided by cos 2x+cos 4x = tan 3x.

Please help I do not understand

Answer 1

\[\frac{ \sin2x+\sin 4x }{ \cos 2x + \cos 4x } = \tan 3x\]

Answer 2

use the sum-to-product formulas.... for the numerator, it is....
\[\sin 2x + \sin 4x = 2 \sin(\frac{ 2x+4x }{ 2 })\cos(\frac{ 2x-4x }{ 2 })\]

Answer 3

for the denominator, it is...
\[\cos 2x + \cos 4x = 2\cos(\frac{ 2x+4x }{ 2 })\cos(\frac{ 2x-4x }{ 2 })\]

Answer 4

if we will combine the expression for both numerator and denominator... the left-hand side will be...
\[\frac{ \sin3x }{ \cos3x } = \tan 3x\]

Answer 5

... this proves equality to the right-hand side of the equation... :-)