Prove that:(cos4x+cos3x+cos2x)/(sin4x+si...

Prove that:`(cos4x+cos3x+cos2x)/(sin4x+sin3x+sin2x)=cot3x`

Text Solution

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`frac{cos 4x+cos3x+cos2x}{sin4x+sin3x+sin2x}=frac{cos4x+cos2x+cos3x}{sin4x+sin2x+sin3x}`
`=frac{(cos4x+cos2x)+cos3x}{(sin4x+sin2x)+sin3x}`
`= (2cos3xcosx+cos3x)/(2sin3xcosx+sin3x)`
`= (cos3x[2cosx+1]) / (sin3x[2cosx+1])` ...

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Knowledge Check

The expression ("cos" 4x+"cos" 3x+"cos"2x)/("sin" 4x+"sin" 3x+ "sin" 2x) is equal to

A

`-cot 3x`

B

cot 3x

C

cot 2x

D

`-cat 2x`

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