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If n is the number of solutions of the equation 2cos x ( 4 s i n ( π 4 + x ) s i n ( π 4 − x ) − 1 ) = 1 ,     x ∈ [ 0 , π ]  and S is the sum of all these solution, then the order pair (n, S) is:

Option 1 -

( 3 ,     5 π ​ / ​ 3 )

Option 2 -

( 2 ,     8 π ​ / ​ 9 )

Option 3 -

( 3 ,     1 3 π ​ / ​ 9 )

Option 4 -

( 2 ,     2 π ​ / ​ 3 ​ )

0 3 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 - 3


    Detailed Solution:

    2 c o s x ( 4 s i n ( π 4 + x ) s i n ( π 4 − x ) − 1 ) = 1  

    ->2cos x (2 cos 2x – 1) = 1

    ⇒ c o s 3 x = 1 2 ,       F o r     0 ≤ x ≤ π , x = π 9 , 5 π 9 , 7 π 9                

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