Question

If tan A = cot(2A - 30°), then what is the value of A?

• A. 30°
• B. 25°
• C. 18°
• D. 40°

Answer 1

Answer:

D. 40°

Given:

$\tan A = \cot(2A - 30^\circ)$

Use the identity:

$\cot \theta = \tan(90^\circ - \theta)$

So,

$\tan A = \tan\big(90^\circ - (2A - 30^\circ)\big)$
$\tan A = \tan(120^\circ - 2A)$
For $(\tan x = \tan y),$

$x = y + n \cdot 180^\circ$

Thus,

$A = 120^\circ - 2A + n \cdot 180^\circ$
$3A = 120^\circ + n \cdot 180^\circ$
$A = 40^\circ + n \cdot 60^\circ$

The principal acute-angle solution is:

$\boxed{40^\circ}$