Question

cosxcos2xcos3x=1/4 prove it
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Answer 1

Step-by-step explanation:

Answer Text

cos(x)cos(2x)cos(3x)=14

⇒4cos(x)cos(2x)cos(3x)=1

⇒(2cosxsinxsinx)⋅2cos(2x)cos(3x)=1

⇒(2sin2xcos2xcos3x)=sinx

⇒sin4xcos3x=sinx

⇒2sin4xcos3x=2sinx

⇒sin7x+sinx=2sinx

⇒sin7x=sinx→(1)

⇒sin7x=sin(π−x)

⇒7x=π−x

⇒x=π8

From (1),

sin7x=sin(π8)

⇒7x=nπ±(−1)n(π8)

⇒x=nπ7±(−1)nπ56

which is generat solution for given equation