Question

If tan 2a = cot (a-18) where 2a is acute angle find value of a

Answer 1

Answer:

36°

Step-by-step explanation:

Given a trignometric equation such that,

tan2a = cot(a-18)

Also, It's given that,

2a is an acute angle.

To find the value of a.

We know that,

For acute angles, we have,

• tan@ = cot(90-@)

Substituting the values,

Therefore, we will get,

=> cot(90-2a) = cot(a-18)

Now, on both the sides,

Trignometric function are same.

Therefore, the angles will also be same.

Therefore, we will get,

=> 90-2a = a-18

=> a +2a = 90+18

=> 3a = 108

=> a = 108/3

=> a = 36

Hence, the required value of a = 36°.

Answer 2

Given,

➠ tan 2A = cot (A – 18°)

As we know by trigonemetric identities,

➠ tan 2A = cot (90° – 2A)

$\longrightarrow$ Substituting the above equation in the given equation, we get;

⇒ cot (90° – 2A) = cot (A – 18°)

Therefore,

⇒ 90° – 2A = A – 18°

⇒ 108° = 3A

A = 108° / 3

Hence, the value of A = 36°