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Rajan@2021
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Write the value of tan1°tan2°……..tan89°.

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One of the most important and conceptual question from trigonometry topic trigonometric identities in which we have to find the value of tan1°tan2°…….tan89° by using trigonometric formulas

Kindly give me a detailed solution of this question as it is already asked in various examinations

RS Aggarwal, Class 10, chapter 13C, question no 28

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1 Answer

  1. tan1tan2tan3...tan89

    =tan1tan2tan3...tan87tan88tan89

    =tan1tan2tan3...tan(903)tan(902)tan(901)

    =tan1tan2tan3...cot3cot2cot1

    =(tan1cot1)(tan2cot2)(tan2cot2)...(tan45cot45)
    since tanθcotθ=1

    =1×1×1×...×1

    =1

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