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# If sec 4A = cosec (A – 20°), where 4A 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.

Given that, sec 4A = cosec (A - 20°) ….(i)

By using property in equation (i) we get:

cosec (90° - 4A) = cosec (A - 20°)

90° - 4A = A - 20°

5A = 110°

A = 110°/5

A = 22°

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

**Video Solution:**

## If sec 4A = cosec (A - 20°), where 4A is an acute angle, find the value of A

Maths NCERT Solutions Class 10 Chapter 8 Exercise 8.3 Question 5

**Summary:**

If sec 4A = cosec (A - 20°), where 4A is an acute angle, then the value of A is 22°.

**☛ Related Questions:**

- Evaluate:(i) sin 18°/cos 72°(ii) tan 26°/cot 64°(iii) cos 48° - sin 42°(iv) cosec 31° - sec 59°
- Show that: (i) tan 48° tan 23° tan 42° tan 67° = 1 (ii) cos 38° cos 52° - sin 38° sin 52° = 0.
- If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.
- If tan A = cot B, prove that A + B = 90°.

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