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  4. The value of ((1+ tan 8°)(1+ tan 37°)/(1+ tan 22°)(1+ tan 23°)) is

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Q. 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

Trigonometric Functions

Solution:

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