Question

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

NCERT Class X
Mathematics - Mathematics

Chapter _INTRODUCTION TO
TRIGONOMETRY

Answer 1

Hi ,

This is related to Trigonometric

Ratios of Complementary angles ,

Two angles are said to be Complementary , if their sum is equal

to 90°.

As you know that ,

Cot ( 90 - x ) = tan x

According to the problem given,

Tan 2A = cot ( A - 18 )

Cot ( 90 - 2A ) = cot ( A - 18 )

Remove the cot both sides

we get ,

90 - 2A = A - 18

-2A - A = - 18 - 90

- 3A = - 108

A = ( - 108 ) / ( - 3 )

A = 36°

I hope this helps you.

:)

Answer 2

given that Tan 2A = cot ( A - 18 )

Cot ( 90 - 2A ) = cot ( A - 18 )

Remove the cot both sides  we get ,

90 - 2A = A - 18

-2A - A = - 18 - 90

- 3A = - 108

A = ( - 108 ) / ( - 3 )

A = 36°