Question

If tan2A = cot (A-40) ,where 2A is an acute angle, find the value of A

Answer 1

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 - 40 )

Cot ( 90 - 2A ) = cot ( A - 40)

Remove the cot both sides

we get ,

90 - 2A = A - 40

-2A - A = - 40 - 90

- 3A = - 130

A = ( - 130) / ( - 3 )

A = 43.3

Answer 2

The value of A is 43.33°.

Step-by-step explanation:

Since we have given that

$\tan 2A=\cot(A-40)\\\\\cot (90-2A)=\cot (A-40)\\\\90-2A=A-40\\\\90+40=A+2A\\\\130=3A\\\\A=\dfrac{130}{3}=43.33^\circ$

Hence, the value of A is 43.33°.

# learn more:

If tan2A=Cot(A+60) find the value of A where 2A is an acute angle

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