Question

prove that cos 9 degrees + sin 9 degrees by cos 9 degrees minus sin 9 degree equals to cos 36°​

Answer 1

Step-by-step explanation:

$\frac{ \cos(9) + \sin(9) }{ \cos(9 ) - \sin(9) } \\ = \frac{ \cos(9) + \sin(9) }{ \cos(9 ) - \sin(9) } \times \frac{ \cos(9) + \sin(9) }{ \cos(9 ) + \sin(9) } \\ = \frac{ { (\cos(9) + \sin(9)) }^{2} }{ { \cos(9) }^{2} - { \sin(9) }^{2} } \\ = \frac{{ \cos(9) }^{2} + { \sin(9) }^{2} + 2 \cos(9) \sin(9) }{ \cos(2 \times 9) } \\ = \frac{1 + \sin(2 \times 9) }{ \cos(18) } \\ \frac{1 + \sin(18) }{ \cos(18) } \\ = \cos(2 \times 18) \\ = \cos(36)$