Question

prove that cos7°-sin7°/cos7°+ sin 7°= tan 38°

Answer 1

Answer

$rhs \\ =\tan(38) \\= \tan(45 - 7) \\ = \frac{ \tan(45) - \tan(7) }{1 + \tan(45) \tan(7) } \\= \frac{1 - \tan(7) }{1 + \tan(7) } \\ =\frac{ \frac{( \cos(7) - \sin(7)) }{ \cos(7) } }{ \frac{ (\cos(7) \sin(7) ) }{ \cos(7) } } \\ = \frac{ \cos(7) - \sin(7) }{ \cos(7) + \sin(7) } \\ hence \: lhs \: = rhs \\ proved \\ formula \: used \: \\ \tan(x - y) = \frac{ \tan(x) - \: \tan(y) }{1 + \tan(x) \tan(y) } \\ \tan(45) = 1 \\ \tan(x) = \frac{ \sin(x) }{ \cos(y) }$

:-)

Answer 2

Step-by-step explanation:

Since tan 7 degree is equals to sin 7degree divide by cos 7degree