Question:
(Sin7x+Sin5x) /(Cos7x+Cos5x)+ /+ (Sin9x+Sin3x) / (Cos9x+Cos3x) =tan 6x
Answer:
Given (Sin7x+Sin5x) /(Cos7x+Cos5x) + (Sin9x+Sin3x) / (Cos9x+Cos3x)
=> [{2*sin(7x+5x)/2 * cos(7x-5x)/2}/{2*cos(7x+5x)/2 * cos(7x-5x)/2}] + [{2*sin(9x+3x)/2 * cos(9x-3x)/2}/{2*cos(9x+3x)/2 * cos(9x-3x)/2}]
=> [{2*sin6x * cosx}/{2*cos6x * cosx}] + [{2*sin6x * cosx}/{2*cos6x * cosx}]
=> (sin6x/cos6x) +(sin6x/cos6x)
=> tan6x + tan6x
=> 2*tan6x
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