Question

If cot(A/2) = tan (A/4 - 18), find A

Answer 1

Answer:

$\cot( \frac{ \alpha }{2} ) = \tan( \frac{ \alpha }{4} - 18 )$

$\tan(90 - \frac{ \alpha }{2} ) = \tan( \frac{ \alpha }{4} - 18 )$

$90 - \frac{ \alpha }{2} = \frac{ \alpha }{4} - 18$

$\frac{ \alpha }{2} + \frac{ \alpha }{4} = 90 + 18$

$\frac{2 \alpha + \alpha }{4} = 108$

$3 \alpha = 108 \times 4 = 432$

$\alpha = \frac{108}{3} = 36$