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Help with a Trigonometric identity...
(sin x + sin 2x + sin 4x) / (cos x + cos 2x + cos 4x) = tan 2x
sin 2x = 2sinxcosx; cos 2x = cos^2x - sin^2x
solving left side,
=[sin x + sin 2x + sin (2x + 2x)]/[cos x + cos 2x + cos (2x+2x)]
=[sin x + sin 2x + 4 sin x*cos^3 x - 4 sin^3 x * cos x] / [cos x + cos 2x + 1 - 6 sin^2 x * cos^2 x]
Cannot go beyond this!
solving right side,
=2 sin x cos x/(cos^2 x - sin^2 x)
=sin 2x/cos 2x
Homework Statement
(sin x + sin 2x + sin 4x) / (cos x + cos 2x + cos 4x) = tan 2x
Homework Equations
sin 2x = 2sinxcosx; cos 2x = cos^2x - sin^2x
The Attempt at a Solution
solving left side,
=[sin x + sin 2x + sin (2x + 2x)]/[cos x + cos 2x + cos (2x+2x)]
=[sin x + sin 2x + 4 sin x*cos^3 x - 4 sin^3 x * cos x] / [cos x + cos 2x + 1 - 6 sin^2 x * cos^2 x]
Cannot go beyond this!
solving right side,
=2 sin x cos x/(cos^2 x - sin^2 x)
=sin 2x/cos 2x