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| 1. |
Prove that sin3x+sin5x+sin7x+sin9x/cos3x+cos5x+cos7x+cos9x=tan6x |
| Answer» We know that sinx+siny=2sinx+y/2•2cosx-y/2 and cosx+cosy=2cosx+y/2cosx-y/2Taking 7x and 5x together and 3xand 9x2sin6x.cosx+2sin6xcos3x/2cos6xcosx+2cos6xcos3x2sin6x(cosx+3x)/2cos6x(cosx+cos3x)Cancelling cosx+3xSin6x/cosx= tanx | |