Question

Let $a=5^{{\log }_5(\sin x)}$ and $b=7^{{\log }_7(\cos x)}$ then $\frac{a}{b}$ can be equal to

• A. $\tan 2^{\circ }$
• B. $\tan 4^{\circ }$
• C. $\tan 5^{\circ }$
• D. $\tan 1^{\circ }$

Answer 1

Answer: (A), (B), (C), (D)

$a=5^{{\log }_5(\sin x)}=\sin x,\sin x>0$ and $b=7^{{\log }_7(\cos x)}=\cos x,\cos x>0$
$\therefore \frac{a}{b}=(\tan x)$, where $x\in I^{st}$ quadrant.