Question

prove that tan70=tan20 + 2tan50

Answer 1

Hi Sayeem

i) tan(20) = tan(70 - 50) = {tan(70) - tan(50)}/{1 + tan(70)*tan(20)}

ii) Cross multiplying, tan(20) + tan(20)*tan(70)*tan(50) = tan(70) - tan(50)

==> tan(20) + tan(50) = tan(70) - tan(50)
[since tan(20) = cot(90 - 20) = cot(70); so tan(20)*tan(70) = cot(70)*tan(70) = 1]

Rearranging the above, tan(20) + 2*tan(50) = tan(70) [Proved]

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