Question : Find the value of $\tan 27^{\circ} \tan 34^{\circ}+\tan 34^{\circ} \tan 29^{\circ}+\tan 29^{\circ} \tan 27^{\circ}$.
Option 1: $0$
Option 2: $–1$
Option 3: $\sqrt3$
Option 4: $1$
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Correct Answer: $1$
Solution :
If $A + B + C = 90°$, then $\tan A\tan B + \tan B\tan C + \tan C\tan A = 1$
Now, 27 + 34 + 29 = 90°
So, $\tan 27^{\circ} \tan 34^{\circ} + \tan 34^{\circ} \tan 29^{\circ} + \tan 29^{\circ} \tan 27^{\circ}=1$
Hence, the correct answer is 1.
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