Oxford Secondary
science
Terry Jen
Answers
Answer:
Explanation:-
Condition:-
Acute angles are less then 90°.
Solution :-
\begin{gathered} \frac{ \cot( \theta) - 1}{ \cot( \theta) + 1} = \frac{1 - \sqrt{3} }{1 + \sqrt{3} } \\ \\ \big( \: \cot( \theta) - 1 \: \big) \big(1 + \sqrt{ 3 } \big) = \big( \: \cot( \theta) + 1 \: \big) \big(1 - \sqrt{ 3 } \big) \\ \\ \cot( \theta) + \sqrt{3} \cot( \theta) - 1 - \sqrt{3} = \cot( \theta) - \sqrt{3} \cot( \theta) + 1 - \sqrt{ 3} \\ \\ \sqrt{3} \cot( \theta) + \sqrt{3} \cot( \theta) = 1 + 1 \\ \\ 2 \sqrt{3} \cot( \theta) = 2 \\ \\ \cot( \theta) = \frac{1}{ \sqrt{3} } \\ \\ \implies \: \cot( \theta) = \cot( \frac{ \pi}{3} ) \\ \\ \implies \: \boxed{ \theta = \frac{ \pi}{3} \: \: o r \: 60 \degree}\end{gathered}
cot(θ)+1
cot(θ)−1
=
1+
3
1−
3
(cot(θ)−1)(1+
3
)=(cot(θ)+1)(1−
3
)
cot(θ)+
3
cot(θ)−1−
3
=cot(θ)−
3
cot(θ)+1−
3
3
cot(θ)+
3
cot(θ)=1+1
2
3
cot(θ)=2
cot(θ)=
3
1
⟹cot(θ)=cot(
3
π
)
⟹
θ=
3
π
or60°