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Grade: 11

                        

Prove that: Tanx tan(x+60)+tanx tan(x-60)+tan(x+60) tan(x-60)=-3

3 years ago

Answers : (1)

Shailendra Kumar Sharma
188 Points
							
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
3 years ago
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