Question

If tan 2A = cot (A – 27), where 2A is an acute angle, find the value of A.​

Answer 1

Answer:

see the picture. it has the solution. hope this helps you

Answer 2

$\huge\mathcal\pink{QUESTION}$

I LET A EQUALS TO

$\alpha$

$\red{tan(2 \alpha ) = \cot(( \alpha - 27)) \\ \\ \\ \\ where \: 2 \alpha \: is \: an \: acute \: angle \: .find \: the \: value \: of \: \alpha}$

$\huge\mathcal\red{ANSWER}$

WE USE THE COMPLEMENTARY TRIGONOMETRIC IDENTITY :

$\brown {tan( \alpha ) = \cot((90 - \alpha ) )}$.

$\tan(2 \alpha ) = \cot(( \alpha - 27) )$

$\cot((90 - 2 \alpha ) ) = \cot(( \alpha - 27) )$

cancelling cot from both sides.

$90 - 2 \alpha = \alpha - 27$

$90 + 27 = \alpha +2 \alpha$

$117 = 3 \alpha$

$\alpha = \frac{117}{3}$

$\alpha = 39$

SO FINAL ANSWER IS 39°.