Q. $\tan{25{^\circ} + \tan{20{^\circ} + \tan{25{^\circ}\tan{20{^\circ}}}}}$ is equal to
A) 1
B) 2
C) 3
D) 4
Explanation
(a)
$\tan{45{^\circ} = \tan{(25{^\circ} + 20{^\circ})}}$
$\Rightarrow \ \ 1 = \frac{\tan{25{^\circ} + \tan{20{^\circ}}}}{1 - \tan{25{^\circ}\tan{20{^\circ}}}}$
$\Rightarrow \ \tan{25{^\circ} + \tan{20{^\circ} + \tan{25{^\circ}\tan{20{^\circ} = 1}}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.