Prove that: $\frac {2sin x}{cos 3x}+ …$ [duplicate]

Prove that: $$\frac {2\sin x}{\cos 3x}+\frac {2\sin 3x}{\cos 9x}+\frac {2\sin 9x}{\cos 27x}=\tan 27x - \tan x$$

My Work,

If we multiply the numerator and denominator of first, second and third term of left hand side by $\cos x$, $\cos 3x$ and $\cos 9x$ respectively and further use the compound angle formula, then we get RHS. But, I want to know if there is any other alternative solution to this problem??

marked as duplicate by S.C.B., Nosrati, lab bhattacharjee trigonometry StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Feb 7 '17 at 8:21

• Note that $\sin x$ is implemented in $\LaTeX$ as \sin x. – S.C.B. Feb 7 '17 at 8:16