Question

Tan100° + 2Tan70°

Please answer this brainly experts​

Answer 1

$\underline{\underline{\mathfrak{\Large{Solution : }}}} \\ \\ \\ \bf\: Tan100\degree + 2 Tan70\degree \\ \\ \\ \bf\: Tan100\degree = \sf\: Tan (90\degree + 10\degree) = - Cot10\degree \\ \\ \\ \bf\:Tan70\degree = \sf\: Tan(90\degree - 20\degree) = Cot20\degree \\ \\ \\ \bf\:Cot20\degree = \sf\: Cot (10\degree + 10\degree)\\ \\ \\ \qquad\sf\dfrac {Cot10\degree \: Cot10\degree - 1}{Cot10\degree + Cot10\degree} = \dfrac {Cot^2 10\degree - 1}{2 Cot10\degree} \\ \\ \\ \bf\implies\: - Cot10\degree + 2 (\dfrac {Cot^2 10\degree - 1}{2 Cot10\degree})\\ \\ \\ \sf\implies\: - Cot10\degree + \dfrac {Cot^2 10\degree}{Cot10\degree} - \dfrac {1}{Cot10\degree} \\ \\ \\ \bf\implies\: - Cot10\degree + Cot10\degree - Tan10\degree \\ \\ \\ \qquad\large {\boxed {\bf { - Tan10\degree}}}$

Answer 2

Answer...

Tan100°+2Tan70°

Tan100°=Tan(90°+10°)=−Cot10°

Tan70°=Tan(90°−20°)=Cot20°

Cot20°=Cot(10°+10°)

Cot10°+Cot10°

Cot10°Cot10°−1

= 2Cot10°Cot 2 10°−1

⟹−Cot10°+2( 2Cot10°Cot 2 10−1 )⟹−Cot10°+ Cot10°

Cot 2 10°

− Cot10°1

⟹−Cot10°+Cot10°−Tan10°

−Tan10°