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The value of tan1° tan2° tan3° ... tan89° is ______. - Mathematics

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प्रश्न

The value of tan1° tan2° tan3° ... tan89° is ______.

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उत्तर

The value of tan1° tan2° tan3° ... tan89° is 1.

Explanation:

tan1° tan2° tan3°… tan89°

= tan1° tan2° … tan45° tan(90° - 44°) tan(90° - 43°) ..…tan(90° - 1°)

= tan1° tan2° … tan45° cot44° cot43° … cot1°   ......[∵ tan(90° - θ) = cotθ]

= tan1° cot1° tan2° cot2°…tan45°… tan89° cot89°

= 1.1….1

= 1

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अध्याय 3: Trigonometric Functions - Exercise [पृष्ठ ५५]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
अध्याय 3 Trigonometric Functions
Exercise | Q 34 | पृष्ठ ५५

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