prove that sin3x + sin5x +sin7x + sin9x / cos3x + cos5x + cos7x +cos9x =tan6x
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Answered by
79
use formula sinC+sinD and cosC+cosD
now (sin3x+sin5x)+(sin7x+sin9x)/(cos3x+cos5x)+(cos7x+cos9x)
=2cosx (sin4x+sin8x)/2cosx (cos4x+cos8x)
=2sin6x cos2x/2cos6x cos2x
=tan6x
now (sin3x+sin5x)+(sin7x+sin9x)/(cos3x+cos5x)+(cos7x+cos9x)
=2cosx (sin4x+sin8x)/2cosx (cos4x+cos8x)
=2sin6x cos2x/2cos6x cos2x
=tan6x
Answered by
30
Hi..
answer in attachment...
#tq
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