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Question

Ife(sin2x+sin2x+sin6x......)loge2andy25y+4=0satisfytheequationthenfindthevalueofsinxcosxsinx

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Solution

Givene(sin2x+sin2x+sin6x......)loge2=elog2(11sin2x)=2(112sin2x)=2sec2x=yNow,y25y+4=0y24yy+4=0y(y4)1(y4)=0(y4)(y1)=0y=4andy=1If2sec2x=1sec2x=0(notpossibleassecx1)else,2sec2x=4sec2x=2cosx=12Thus,thevalueofsinxcosxsinx=121212Notdefined.

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