Prove that cos6x+6cos4x+15cos2x+10/cos5x+5cos3x+10cosx= 2cosx
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L.H.S = cos 6x + 6 cos 4x + 15 cos 2x + 10/ cos 5x + 5 cos 3x + 10 cos x
= cos 6x + cos 4x + 5 cos 4x + 5 cos 2x + 10 cos 2x + 10/ cos 5x + 5 cos 3 x + 10 cosx
as cos 6x + cos 4x = 2 cos 5x cosx ; cos 4 x + cos 2x = 2 cos 3 xcosx; cos 2 x + cos 0 = 2 cosxcosx
= 2 cos 5xcosx + 5 (2 cos 3 xcosx) + 10 (2 cosxcosx)/ cos 5x + 5 cos 3 x + 10 cos x
= 2 cos x (cos 5x + 5 cos 3x + 10 cosx)/ cos 5x + 5cos 3x + 10 cosx
= 2 cosx
= R.H.S
= cos 6x + cos 4x + 5 cos 4x + 5 cos 2x + 10 cos 2x + 10/ cos 5x + 5 cos 3 x + 10 cosx
as cos 6x + cos 4x = 2 cos 5x cosx ; cos 4 x + cos 2x = 2 cos 3 xcosx; cos 2 x + cos 0 = 2 cosxcosx
= 2 cos 5xcosx + 5 (2 cos 3 xcosx) + 10 (2 cosxcosx)/ cos 5x + 5 cos 3 x + 10 cos x
= 2 cos x (cos 5x + 5 cos 3x + 10 cosx)/ cos 5x + 5cos 3x + 10 cosx
= 2 cosx
= R.H.S
Answered by
57
Given,
cos6x+6cos4x+15cos2x+10/cos5x+5cos3x+10cosx= 2cosx
L.H.S = cos 6x + 6 cos 4x + 15 cos 2x + 10/ cos 5x + 5 cos 3x + 10 cos x
= cos 6x + (cos 4x + 5 cos 4x) + (5 cos 2x + 10 cos 2x) + 10/ cos 5x + 5 cos 3 x + 10 cosx
= 2 cos 5xcosx + 5 (2 cos 3 xcosx) + 10 (2 cosxcosx)/ cos 5x + 5 cos 3 x + 10 cos x
= 2 cos x (cos 5x + 5 cos 3x + 10 cosx)/ cos 5x + 5cos 3x + 10 cosx
= 2 cosx
= R.H.S
cos6x+6cos4x+15cos2x+10/cos5x+5cos3x+10cosx= 2cosx
L.H.S = cos 6x + 6 cos 4x + 15 cos 2x + 10/ cos 5x + 5 cos 3x + 10 cos x
= cos 6x + (cos 4x + 5 cos 4x) + (5 cos 2x + 10 cos 2x) + 10/ cos 5x + 5 cos 3 x + 10 cosx
= 2 cos 5xcosx + 5 (2 cos 3 xcosx) + 10 (2 cosxcosx)/ cos 5x + 5 cos 3 x + 10 cos x
= 2 cos x (cos 5x + 5 cos 3x + 10 cosx)/ cos 5x + 5cos 3x + 10 cosx
= 2 cosx
= R.H.S
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