Question

The value of $\frac{\left(1+\tan 8^{\circ }\right)\left(1+\tan 37^{\circ }\right)}{\left(1+\tan 22^{\circ }\right)\left(1+\tan 23^{\circ }\right)}$ is

• A. 0
• B. 2
• C. 8
• D. 1

Answer 1

Answer: (D)

$37^{\circ }=45^{\circ }-8^{\circ }$
$\Rightarrow \tan 37^{\circ }=\frac{1-\tan 8^{\circ }}{1+\tan 8^{\circ }}$
$\Rightarrow 1+\tan 37^{\circ }=\frac{2}{1+\tan 8^{\circ }}$
Similarly $1+\tan 23^{\circ }=\frac{2}{1+\tan 22^{\circ }}$
$\therefore \frac{\left(1+\tan 8^{\circ }\right)\left(1+\tan 37^{\circ }\right)}{\left(1+\tan 22^{\circ }\right)\left(1+\tan 23^{\circ }\right)}=1$