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Prove that tanxtan(x+60)+tan(x+60)tan(x-60)+tanxtan(x-60)=-3

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Prove that tanxtan(x+60)+tan(x+60)tan(x-60)+tanxtan(x-60)=-3

Posted by Bhavesh Kumar 6 years, 9 months ago

CBSE > Class 11 > Mathematics

1 answers

Gaurav Seth 4 years, 4 months ago

Tan(A-B) =TanA-TanB/(1+TanATanB) => TanATanB+1=(TanA-TanB)/Tan(A-B) So TanxTan(60+x)+1 ={Tan(60+x)-Tan60}/Tan60 -----1 Tanxtan(x-60)+1= {Tanx- Tan(60-x)}/tan60---------2 Tan(x+60)tan(x-60)+1 ={tan(60+x)-tan(x-60)}/tan120--------3 Adding 1,2 and 3 we get TanxTan(60+x)+1+Tanxtan(x-60)+1+Tan(x+60)tan(x-60)+1=0 soTanx tan(x+60)+tanx tan(x-60)+tan(x+60) tan(x-60)=-3

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