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Inverse Trigonometric Functions Test - 8

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Inverse Trigonometric Functions Test - 8
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  • Question 1
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    tan x is periodic with period  

     

    Solution

     

     

    The values of tan x repeats after an interval of  π.

     

     

  • Question 2
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    Solution

     

     

     

     

  • Question 3
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     is equal to  

     

    Solution

     

     




     

     

  • Question 4
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    Solution

     

     


     

     

  • Question 5
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    Solution

     

     

    The correct option is B.

     

     

  • Question 6
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    The period of the function  f(x) = tan 3x is

     

    Solution

     

     

    f(x) = tan 3x, as the period of tan x = π. 3x = x = π/3.

     

     

  • Question 7
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    The range of  tan−1 x is

     

    Solution

     

     

    The range of tan−1 x is given by -π/2  to  π/2

     

     

  • Question 8
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    The value of    is (a, b >0)

     

    Solution

     

     



     

     

  • Question 9
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    The solution of the equation  

     

    Solution

     

     



    But , x= -1/2 does not satisfy the given equation.

     

     

  • Question 10
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     is equal to  

     

    Solution

     

     

    = tan-1  a - tan-1   b + tan-1 c + tan-1 c - tan-1 a

     

     

  • Question 11
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    sin2 250 +sin2 650  is equal to

     

    Solution

     

     

    sin2 250 + sin2 650 = cos2 650 + sin2 650 = 1

     

     

  • Question 12
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    If  θ= tan−1 x then sin 2 θis equal to

     

    Solution

     

     

    As we know that : sin 2 θ=  , now if  θ= tan-1 x ⇒x = tan θ⇒sin 2 θ= 

     

     

  • Question 13
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    if x >0, then tan-1 x + tan-1 (1/x) is equal to

     

    Solution

     

     

     

     

  • Question 14
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    Solution

     

     

     

     

  • Question 15
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    If and  x  + y  + z  = xyz, then a value of  tan−1 x+tan−1 y+tan−1 z is

     

    Solution

     

     

     

     

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