Question

If tan 2A=cot (A-180) where 2A is an acute angle Find the value of A

Answer 1

2A=cot(A-180)

cot(90-2A)=cot(A-180)

90-2A=A-180

90+180=2A+A

270=3A

A=270/3

A=90

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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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