Question

If tan 2A=cot(A-18), where 2A is an acute angle, find the value of A.

Answer 1

Solution: tan2A=cot(A-18
or, cot(90-2A)=cot(A-18). {since tan A=cot(90-A)}
or, 90-2A=A-18
or,. 90+18=A+2A
or,. 108=3A
or,. A=108/3
or,. A= 36° answer

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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