Question 934107: tan20°+2 tan50°=
Answer by srinivas.g(540)   (Show Source):
You can put this solution on YOUR website! We know, tan(90)=tan (70+20)=infinity =1/0 = [ tan(70) + tan(20) ] / [ 1 - tan(70).tan(20) ].
Therefore, 1 - tan(70).tan(20) = 0
So, tan(70).tan(20) = 1 ...(A)
Expanding tan(70) = [ tan(50) + tan(20) ] / [ 1- tan(50).tan(20) ].
Therefore, tan(50) + tan(20) = tan(70) * [ 1- tan(50).tan(20) ].
that is, tan(50) + tan(20) = tan(70) - tan(70).tan(50).tan(20).
that is, 2.tan(50) + tan(20) = tan(50) + tan(70) - tan(70)tan(50).tan(20).
= tan(50) + tan(70) - tan(50) ....[ from equation (A) ]
= tan(70).
result is tan 70
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