provethat: cos5x−cosxsin5x−2sin3x+sinx=tanx

LHS: =cos5x−cosxsin5x−2sin3x+sinx=cos5x−cosx[(sin5x−sin3x)−(sin3x−sinx)]=−2sin3xsin2x[(2cos4xsinx)−(2cos2xsinx)]=−2sin3x.2sinxcosx2sinx(cos4x−cos2x)=−2sin3xcosxcos4x−cos2x=−2sin3xcosx−2sin3xsinx=cosxsinx=tanx = RHS

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prove that: { sin5x-2sin3x+sinx }{ cos5x-cosx } =tanx

Question

$p ro v e t ha t : \frac{s in 5 x - 2 s in 3 x + s in x}{cos 5 x - cos x} = t an x$

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p ro v e t ha t : \frac{s in 5 x - 2 s in 3 x + s in x}{cos 5 x - cos x} = t an x

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Text solutionVerified

LHS:

= \frac{s in 5 x - 2 s in 3 x + s in x}{cos 5 x - cos x}

= \frac{[( s in 5 x - s in 3 x ) - ( s in 3 x - s in x )]}{cos 5 x - cos x}

= \frac{[( 2 cos 4 x s in x ) - ( 2 cos 2 x s in x )]}{- 2 s in 3 x s in 2 x}

= \frac{2 s in x ( cos 4 x - cos 2 x )}{- 2 s in 3 x .2 s in x cos x}

= \frac{cos 4 x - cos 2 x}{- 2 s in 3 x cos x}

= \frac{- 2 s in 3 x s in x}{- 2 s in 3 x cos x}

= \frac{s in x}{cos x} = t an x

= RHS

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Question Text	$p ro v e t ha t : \frac{s in 5 x - 2 s in 3 x + s in x}{cos 5 x - cos x} = t an x$
Answer Type	Text solution:1
Upvotes	150

provethat: cos5x−cosxsin5x−2sin3x+sinx​=tanx

Text solutionVerified

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$p ro v e t ha t : \frac{s in 5 x - 2 s in 3 x + s in x}{cos 5 x - cos x} = t an x$