Question

if tan2a =cot a(a-80°)where 2a is acute angle.find A.

Answer 1

tan 2a=cot 90-(a-80)
tan2a=cot90-a+80
tan2a=tana+170
2a+a=170
3a=170
a=170/3

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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