cos x cos 2x cos 4x cos 8x =(sin 16x...

`cos x cos 2x cos 4x cos 8x =(sin 16x)/(16sin x)`

Text Solution

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LHS `=(1)/(2 sin x) " (2 sin x cos x ) cos 2 x cos cos 4x cos 8x "`
`=(1)/(2 sin x) "( sin 2x cos 2x) cos 4x cos 8x "`
`=(1)/(4 sin x) "(2 sin 2x cos 4x) cos 8x "`
`=(1)/(4 sin x) " (sin 4x cos 4x ) cos 8x "`
`=(1)/(8 sin x) " (2 sin 4x cos 4x ) cos 8x "`
`=(1)/(8 sin x) " (sin 8x cos 8x ) "`
`=(1)/(16 sin x) " (2 sin 8x cos 8x) "`
`=(1)/(16 sin x) " (sin 16 x) " =(sin 16x)/(16 sin x) =RHS`

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prove that cos x cos2x cos4x cos8x=(sin16x)/(16sin x)

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Knowledge Check

The general solution of the equation 8 cos x cos 2x cos 4x = sin 6x//sin x is

A

`x=(n pi//7)+(pi//21), AA n in Z`

B

`x=(2pi//7)+(pi//14), AA n in Z`

C

`x=(n pi//7)+(pi//14), AA n in Z`

D

`x=(n pi)+(pi//14), AA n in Z`

(" sin 8x cos x- sin 6x cos 3x")/(" cos 2x cos x - sin 4x sin 3x")=

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` " sin " 2x`

B

` " cos " 2x`

C

` " tan " 2x`

D

` " cosec " 2x`

if f(x) = cos x cos 2x cos 4x cos 8 x cos 16 x , then f' (pi //4) is

A

`1`

B

` sqrt(2)`

C

`1 // sqrt(2)`

D

None

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