What is the value of \(\tan 7^\circ\tan 14^\circ\tan 21^\circ\tan 28^\circ\tan 83^\circ\tan 76^\circ\tan 69^\circ\tan 62^\circ\)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1
For complementary angles \(\tan(90^\circ-A)=\cot A\), and \(\tan A\cot A=1\). The eight angles form four complementary pairs.
Pairs: \(7^\circ+83^\circ\), \(14^\circ+76^\circ\), \(21^\circ+69^\circ\), \(28^\circ+62^\circ\), each \(90^\circ\)
\(\tan 7^\circ\tan 83^\circ=\tan 7^\circ\cot 7^\circ=1\), and the same for each pair
Product \(=1\times1\times1\times1=1\)