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If tan A = 1/√3, find all other trigonometric ratios of angle A.

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This is an important question from

Book- ML Aggarwal
Board- ICSE
Publication- Avichal
Chapter- Trigonometric Identities

This question has been asked in previous year exam

If tan A = 1/root3, find all other trigonometric ratios of angle A.

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ML Aggarwal book, ICSE board, ques no. 4th

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1 Answer

  1. Solution:

    Given, tan A = 1/√3

     

    In right ∆ ABC,

     

    tan A = BC/AB = 1/√3

     

    So,

     

    BC = 1 and AB = √3

     

    By Pythagoras theorem,

     

    AC = √(AB²+ BC²) = √[(√3)² + (1)²]

     

    = √(3 + 1) = √4 = 2

     

    Hence,

     

    sin A = BC/AC = ½

     

    cos A = AB/AC = √3/2

     

    cot A = 1/tan A = √3

     

    sec A = 1/cos A = 2/√3

     

    cosec A = 1/sin A = 2/1 = 2

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