Question

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Answer 1

Answer:

How do I prove that cos 5x + cos 4x / 1-2 cos 3x = -(cos 2x + cosx)?

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LHS=(cos5x +cos4x)/(1–2cos3x)

={2cos(9x/2) cos(x/2)}/(1–2cos3x)

Above and below multiple by cos(3x/2)

=(2cos9x/2 cosx/2 cos3x/2 ) /(cos3x/2 -2cos3x cos3x/2 )

=(2cos9x/2 cosx/2 cos3x/2 )/(cos3x/2 -cos9x/2 -2cos3x/2 )

=(2cos9x/2 cosx/2 cos3x/2 ) /(-cos9x/2)

=-(2cos3x/2 cosx/2 )

=-(cos2x +cosx) RHS

Step-by-step explanation:

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Answer 2

Answer:

LHS=(cos5x +cos4x)/(1–2cos3x)

={2cos(9x/2) cos(x/2)}/(1–2cos3x)

Above and below multiple by cos(3x/2)

=(2cos9x/2 cosx/2 cos3x/2 ) /(cos3x/2 -2cos3x cos3x/2 )

=(2cos9x/2 cosx/2 cos3x/2 )/(cos3x/2 -cos9x/2 -2cos3x/2 )

=(2cos9x/2 cosx/2 cos3x/2 ) /(-cos9x/2)

=-(2cos3x/2 cosx/2 )

=-(cos2x +cosx) RHS