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The value of tan1°tan2°tan3° ........tan89° is
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- 1
- - 1
- 0
- None of the options
Correct Option: A
tan (90° – θ) = cotθ tanθ.cotθ = 1
tan 89° = tan (90° – 1°) = cot 1°.
tan 88° = tan (90° – 2°) = cot 2°.
∴ Expression = (tan 1°.tan 89°) (tan 2°.tan 88°) ---- tan 45°
= (tan 1°.cot 1°). (tan 2°.cot 2°) ---- tan 45°
= 1.1 ----1 = 1
