Question

Q. If tan 2A = cot (A - 189) then
find the value of A.
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Answer 1

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Solution :

Given,

tan 2A = cot (A - 18°)

tan 2A = tan (90° - (A - 189)]

tan 2A = tan (108° – A]

=>2A = 108° - A

=>3A = 108°

=> A =108°/3

=>36°

Answer 2

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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.