The value of tan 1°.tan 2° tan 3° equal to
The value of tan 1°.tan 2° tan 3° equal to
(A) -1
(B) 1
(C) π/2
(D) 2
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Correct answer is (B) 1
Explanation :
tan1° tan2° tan3° … tan89°
= (tan 1° tan 89°) (tan 2° tan 88°)
…(tan 44° tan 46°) tan 45°
= (tan 1 ° cot 1 °) (tan 2° cot 2°)
…(tan 44° cot 44°) . tan 45°
…tan(∵ 90° – θ) = cot θ]
= 1 x 1 x 1 x … x 1 x tan 45° = 1
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