सिध्द कीजिए कि : ` (sin 5 x - 2 sin 3 x + sin x)/(cos 5 x - cos x) `=tanx

Explanation

`(sin 5x- 2sin 3x + sin x)/(cos 5x – cos x) = (sin 5x+ sin x-2 sin 3x)/(cos 5x – cos x)`
` = (2 sin .((5x+x)/(2)) cos. ((5x-x)/(2))- 2 sin 3x)/(-2 sin .((5x+x)/(2)) sin.((5x-x)/(2))`
`= (2 sin 3x cos 2x -2 sin 3x)/(-2 sin 3x sin 2x)`
` = (2 sin 3x (cos 2x -1))/( - 2 sin 3x sin 2x)`
`= (1- cos 2x)/(sin 2x) = (2 sin^(2)x)/(2 sin x cos x)`
`= (sin x)/(cos x) = tan x `= दायाँ पक्ष