Express cos7xcos2x in the form of A(cosBx+cosCx) where A,B and C are constants to be determined.

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14-06-2017
Mathematics

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Express cos7xcos2x in the form of A(cosBx+cosCx) where A,B and C are constants to be determined.

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LammettHash LammettHash · Answer 1 · 2017-06-15T19:28:32+02:00

LammettHash LammettHash

15-06-2017

[tex]\cos(7x+2x)=\cos7x\cos2x-\sin7x\sin2x[/tex]
[tex]\cos(7x-2x)=\cos7x\cos2x+\sin7x\sin2x[/tex]

[tex]\implies\cos9x+\cos5x=2\cos7x\cos2x[/tex]
[tex]\implies\cos7x\cos2x=\dfrac12(\cos9x+\cos5x)[/tex]
[tex]\implies A=\dfrac12,B=9,C=5[/tex]

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