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.

tan (90° - θ) = cot θ

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°.

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