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 If cot a = 1 and sec b = − 5 3 , where   π < α < 3 π 2     a n d     π 2 < β < π , then the value of tan(a + b) and the quadrant in which a + b lies, respectively are:

Option 1 -

− 1 7 and IVth quadrant 

Option 2 -

7 and Ist quadrant         

Option 3 -

-7 and IVth quadrant   

Option 4 -

  1 7 and Ist quadrant

0 2 Views | Posted 2 months ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    2 months ago
    Correct Option - 1


    Detailed Solution:

    cota = 1        & secβ =   − 5 3

    < <        3 π 2  secβ =   − 5 3

    α = ( π + π 4 )  cosβ = − 3 5 = c o s ( 1 8 0 − 5 3 )  

    tanb =  − 4 3  

    tan(α + β) =   t a n α + t a n β 1 − t a n α t a n β

    ∴ A − 1 4 & 4 t h     q u a d r a n t .

    = 1 − 4 3 1 + 4 3 = − 1 7

    ∴ − 1 4 & 4 t h     q u a d r a n t .

                   

                   

                   

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