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# If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A

**Solution:**

We will be using the trigonometric ratios of complementary angles to solve the given question.

tan (90° - θ) = cot θ

Given that:

tan 2A = cot (A - 18°) ….(i)

But tan 2A = cot (90° - 2A)

By substituting this in equation (i) we get:

cot (90° - 2A) = cot (A - 18°)

90° - 2A = A - 18°

3A = 108°

A = 108°/3

A = 36°

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 8

**Video Solution:**

## If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A

Maths NCERT Solutions Class 10 Chapter 8 Exercise 8.3 Question 3

**Summary:**

If tan 2A = cot (A - 18°), where 2A is an acute angle, then the value of A is 36°.

**☛ Related Questions:**

- If tan A = cot B, prove that A + B = 90°.
- If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A.
- If A, B and C are interior angles of a triangle ABC, then show that: sin (B + C)/2 = cos A/2
- Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

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