Prove the following: cos 27°+ sin 27°/ cos 27° - sin 27° = tan 72°

Question

Prove the following:

\(\frac {cos\, 27°+sin\,27°}{cos\,27°-sin\,27°} = tan\, 72°\)

cos 27°+ sin 27°/ cos 27° - sin 27° = tan 72°

Answer 1

\(\frac {cos\, 27°+sin\,27°}{cos\,27°-sin\,27°}\)

Dividing numerator and cos 27°, we get denominator by cos 27°, we get

= tan (45° + 27°) 

= tan 72° = R.H.S