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Question
Select the correct option from the given alternatives:
The value of tan1°.tan2°tan3°..... tan89° is equal to
Options
– 1
1
`pi/2`
2
Solution
1
Explanation:
tan1° tan2° tan3° ...... tan89°
= (tan1° tan89°) (tan2° tan88°) .....(tan44° tan46°)tan45°
= (tan1° cot1°) (tan2° cot2°) ...(tan44° cot44°) . tan45° ....[∵ tan(90° − θ) = cot θ]
= 1 × 1 × 1 × ..... × 1 × tan45° = 1
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