Question

P.T.
tan 70° = 2 tan 50° + tan 20°​

Answer 1

Answer:

70 = 20 +50

So tan 70 = tan (20 +50)

Tan70 = (tan20 + tan50) / (1 - tan20 tan50)

(Tan70) (1 - tan20 tan50) = (tan20 + tan50)

Tan70 - Tan70 tan20 tan50 = (tan20 + tan50)

Tan70 tan20 =1

Tan70 - 1. Tan50 = tan20 + tan50

Tan 70 = tan20 + tan50 + tan50

Tan 70 = tan20 + 2 tan50

Hence proved

Answer 2

tan 70° = 2 tan 50° + tan 20°

Taking LHS.

tan50 = tan (50+20)

$\frac{ \tan(70) }{1} = \frac{ \tan(50) + \tan(20) }{1 - \tan(50) \tan(20) }$

tan70 - tab70•tan50•tan20 = tan50 + tan20

tan70 - tan70 × tan50 × cot70 = tan50 + tan20

tan70 - tan50 = tan50 + tan 20

tan70 = 2tan50 + tan20

LHS = RHS. Hence proved.

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