Find the value of \(\displaystyle{9}{\tan{{\left\lbrace{10}^{{\circ}}\right\rbrace}}}+{2}{\tan{{\left\lbrace{20}^{{\circ}}\right\rbrace}}}+{4}{\tan{{\left\lbrace{40}^{{\circ}}\right\rbrace}}}-{\tan{{\left\lbrace{80}^{{\circ}}\right\rbrace}}}\)

Joaquin Salas

Joaquin Salas

Answered question

2022-04-08

Find the value of 9tan{10}+2tan{20}+4tan{40}tan{80}

Answer & Explanation

libertydragonrbha

libertydragonrbha

Beginner2022-04-09Added 15 answers

with the help of
tanθ=cotθ2cot2θ
Replace θ2θ , we have
2tan2θ=2cot2θ4cot(4θ)
similarly
4tan(4θ)=4cot(4θ)4cot(8θ)
So
tanθ+2tan2θ+2tan4θ=8cot(8θ)
put θ=10
tan10+2tan20+4tan40=cot(10)8cot(80)=tan(80)8tan(10)
9tan10+2tan20+4tan40tan(10)=0

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