Maharashtra State BoardHSC Science (General) 11th
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Select the correct option from the given alternatives: The value of tan1°.tan2°tan3°..... tan89° is equal to - Mathematics and Statistics

MCQ

Select the correct option from the given alternatives:

The value of tan1°.tan2°tan3°..... tan89° is equal to

Options

  • – 1

  • 1

  • `pi/2`

  • 2

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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

Concept: Fundamental Identities
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 2 Trigonometry - 1
Miscellaneous Exercise 2 | Q I. (10) | Page 33
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