Question

if tan 2A=(A-18)where 2A is an acute angle find the value of A

Answer 1

tan2A=(A-18)
tan2A=tan (90-A+18)
2A=-A+108
3A=108
A=36

Answer 2

 Solution:

It is given that tan2A=cot(A−18°)

 ⇒tan2A=cot(90° −(108° −A))

⇒tan2A=tan(108° −A)        

{°•° cot(90° −A)=tan(A)}

 ⇒2A=108° −A

 ⇒3A=108°

 ⇒A=108°/3 =36°

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