how to solve this limit \(\displaystyle\lim_{{\theta\to{0}}}{\frac{{{\tan{{\left({5}\theta\right)}}}}}{{{\tan{{\left({10}\theta\right)}}}}}}\)

Jaylin Clements 2022-03-29 Answered
how to solve this limit limθ0tan(5θ)tan(10θ)
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Answers (2)

glikozyd3s68
Answered 2022-03-30 Author has 16 answers
limθ0tan5θtan10θ=limθ0(sin5θ5θ10θsin10θ5θ10θcos10θcos5θ)=12
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zevillageobau
Answered 2022-03-31 Author has 13 answers
Call x=5θ and note that
limθ0tan5θtan10θ=limx0tanxtan2x=limx0tanx2tanx1tan2x
=12limx0(1tan2x)=
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