Question

Please answer with proper explanation

Answer 1

Answer:

1

Step-by-step explanation:

I will be using a,b,c,d instead of α1,α2,α3α4 as it is difficult to type.

$\frac{ \cos(a - b) }{ \cos(a + b) } + \frac{ \cos(c - d) }{ \cos(c + d) } \: = 0$

$\frac{\cos(a - b)\cos(c + d)+ \cos(c - d)\cos(a + b) }{ \cos(a + b) \cos(c + d) }= 0$

$\cos(a - b) \cos(c + d) + \cos(a + b) \cos(c - d) = 0$

$( \cos(a) \cos(b) + \sin(a) \sin(b))( \cos(c ) \cos(d) - \sin(c) \sin(d)) + ( \cos(a ) \cos(b) - \sin(a) \sin(b)).( \cos(c ) \cos(d) + \sin(c) \sin(d)). = 0$

$\cos(a) \cos(b) \cos(c) \cos(d) -\cos(a) \cos(b) \sin(c) \sin(d) +\sin(a) \sin(b) \cos(c) \cos(d) -\sin(a) \sin(b) \sin(c) \sin(d) + \cos(a) \cos(b) \cos(c) \cos(d) +\cos(a) \cos(b) \sin(c) \sin(d) -\sin(a) \sin(b) \cos(c) \cos(d) -\sin(a) \sin(b) \sin(c) \sin(d) = 0$

$2 \cos(a) \cos(b) \cos(c) \cos(d) - 2 \sin(a) \sin(b) \sin(c) \sin(d) = 0$

$\sin(a) \sin(b) \sin(c) \sin(d) = \cos(a) \cos(b) \cos(c) \cos(d)$

$\frac{ \sin(a) \sin(b) \sin(c) \sin(d) }{ \cos(a) \cos(b) \cos(c) \cos(d) } = 1$

$\tan(a) \tan(b) \tan(c) \tan(d) = 1$