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8. Introduction to Trigonometry
medium
If $\tan 2 A=\cot \left(A-18^{\circ}\right),$ where $2 A$ is an acute angle, find the value of $A .$ (in $^{\circ}$)
A
$108$
B
$90$
C
$18$
D
$36$
Solution
Given that,
$\tan 2 A=\cot \left(A-18^{\circ}\right)$
$\cot \left(90^{\circ}-2 A \right)=\cot \left( A -18^{\circ}\right)$
$90^{\circ}-2 A = A -18^{*}$
$108^{\circ}=3 A$
$A=36^{\circ}$
Standard 10
Mathematics