If tan 2 A=cot left(A-18^{circ}right), where 2 A is an acute angle, value of A . (in ^{circ} )

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8. Introduction to Trigonometry

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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

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