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Consider the equation .

Statement 1: Solution of this equation is cos .

Statement 2: This equation has only one real solution.

Option 1 -

Both statement 1 and statement 2 are true

Option 2 -

Statement 1 is true but statement 2 is false

Option 3 -

Statement 1 is false but statement 2 is true

Option 4 -

Both statement 1 and statement 2 are false

0 2 Views | Posted a month ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    a month ago
    Correct Option - 2


    Detailed Solution:

    12x =

      3 x = π 4

    c o s 3 x = 1 2

    4 c o s 3 x − 3 c o s x = 1 2

    4 2 c o s 3 x − 3 2 c o s x − 1 = 0            

    x = π 1 2 is the solution of above equation.

    Statement 1 is true

    f ( x ) = 4 2 x 3 − 3 2 x − 1

    f ' ( x ) = 1 2 2 x 2 − 3 2 = 0

    x = ± 1 2

    f ( − 1 2 ) = − 1 2 + 3 2 − 1 = 2 − 1 > 0            

    f(0) = – 1 < 0

    one root lies in ( − 1 2 ,   0 ) , one root is c o s π 1 2  which is positive. As the coefficients are real, therefore all the roots must be real.

    Statement 2 is false.

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Option (4) is correct.

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A
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