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# If tan A = cot B, prove that A + B = 90°

**Solution:**

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

Given that: tan A = cot B .... (i)

We know that tan A = cot (90° - A)

By substituting this in equation (i) we get:

cot (90° - A) = cot B

90° - A = B

A + B = 90°

Hence proved A + B = 90°.

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

**Video Solution:**

## If tan A = cot B, prove that A + B = 90°.

Maths NCERT Solutions Class 10 Chapter 8 Exercise 8.3 Question 4

**Summary:**

If tan A = cot B, then it is proved that A + B = 90°.

**☛ 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 sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A.

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