Question

Prove that : (cos29degrees+sin29degree)\cos29degree-sin29degree=tan74degree

Answer 1

$\frac{ \cos(29) + \sin(29) }{ \cos(29) - \sin(29) } \\ = \frac{1 + \frac{ \sin(29) }{ \cos(29) } }{1 - \frac{ \sin(29) }{ \cos(29) } } \\ = \frac{1 + \tan(29) }{1 - \tan(29) } \\ = \frac{ \tan(45) + \tan(29) }{1 - (\tan(45) \times \tan(29)) } \: \: \: \: ( \tan(45) = 1) \\ = \tan(45 + 29) \\ = \tan(74)$