The value of tan 1° tan 2° tan 3° ... tan 89° is
The value of tan 1° tan 2° tan 3° ... tan 89° is
(A) 0
(B) 1
(C)1/2
(D) Not defined
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1 Answers
Answer is (B)
tan 1° tan 2° tan 3° … tan 89°
= [tan 1° tan 2° … tan 44°] tan 45°[tan (90° – 44°) tan (90° – 43°)… tan (90° – 1°)]
= [tan 1° tan 2° … tan 44°] [cot 44° cot 43°……. cot 1°]
=[tan 1°*cot 1°* tan 2°*cot 2°.....] (tan 1°*cot 1° = 1)
= 1*1… 1*1 = 1
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Answered