Question

$\tan 54°$ can be expressed as

• A. $\frac{(\cos 9°+\sin 9°)}{(\cos 9°–\sin 9°)}$
• B. $\frac{(\cos 9°-\sin 9°)}{(\cos 9°+\sin 9°)}$
• C. $\frac{(\sin 9°-\cos 9°)}{(\cos 9°+\sin 9°)}$
• D. None of these

Answer 1

The correct option is A

$\frac{(\cos 9°+\sin 9°)}{(\cos 9°–\sin 9°)}$

Solving function using trigonometric identities:

We know, $\tan (A+B)=\frac{(\tan A+\tan B)}{(1–\tan A\tan B)}$

$\tan 54°=\tan (45+9)°$

$=\frac{(\tan 45°+\tan 9°)}{(1–\tan 45°\tan 9°)}$

$=\frac{(1+\tan 9°)}{(1–\tan 9°)}$

$=\frac{\left(1+{\displaystyle \frac{\sin 9°}{\cos 9°}}\right)}{\left(1–{\displaystyle \frac{\sin 9°}{\cos 9°}}\right)}$

$=\frac{(\cos 9°+\sin 9°)}{(\cos 9°–\sin 9°)}$

Hence, the option (A) is the answer.