Question

if tan (2a) = cot (a 18), where 2a is an acute angle,, find the value of a.

Answer 1

hey i think there is a correction in this question: if yes then it is cot(a-18°)instead of cot(a18)

tan(2a) = cot(a - 18°)

cot(90 - 2a) = cot(a - 18°)

90 - 2a = a - 18°

3a = 108°

a = 36°

if my correction is wrong then the question will be:

tan(2a) = cot(18a)

tan(2a) = tan(90-18a)

2a = 90-18a

a = 9/2

HEY MATE I HAVE SOLVED THIS QUESTION IN BOTH WAYS.

HOPE THIS WILL HELP PLEASE MARK AS BRAINLIEST AND FOLLOW ME.

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°

Thanks ☺