Question

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

Answer 1

`\cos(7x+2x)=\cos7x\cos2x-\sin7x\sin2x`

`\cos(7x-2x)=\cos7x\cos2x+\sin7x\sin2x`


`\implies\cos9x+\cos5x=2\cos7x\cos2x`

`\implies\cos7x\cos2x=\frac12(\cos9x+\cos5x)`

`\implies A=\frac12,B=9,C=5`