Question:
The value of tan 1° tan 2° tan 3°… tan 89° is
A. 0
B. 1
C. ½
D. Not defined
Solution:
B. 1
Explanation:
According to the question,
tan 1° tan 2° tan 3°… tan 89°
= tan 1° tan 2° … tan 45° tan (90-44°) tan(90-43°)…tan (90-1°)
= tan 1°tan 2° … tan 45°cot 44°cot 43°…cot 1° [∵tan (90-θ)=cot θ]
= tan 1° cot 1° tan 2° cot 2°…tan45°… tan 89° cot 89°
=1.1….1 = 1
Thus, option (B) 1 is the correct answer.
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