If the equation 2ksinx + 7 = 4k - cos2x possesses a solution for k E [a, b], then (a + b) is equal to
Answers
Given : equation 2ksinx + 7 = 4k – cos2x possesses a solution for k ∈ [a , b]
To Find : (a + b) value
Solution:
2ksinx + 7 = 4k - cos2x
=> 2ksinx + 7 = 4k - (1- 2sin²x)
=> 2ksinx + 7 = 4k - 1 + 2sin²x
=> 2sin²x - 2ksinx + 4k - 8 = 0
=> sin²x - ksinx + 2k - 4 = 0
Sinx = (k ± √(k² - (4(2k-4)) ) /2
=> Sinx = (k ± √(k² - 8k + 16 ) /2
=> Sinx = (k ± √(k - 4)² ) /2
=> Sinx = (k + k - 4) /2 , ( k - k + 4)/2
=> sinx = (2k - 4)/2 , 2 ( not possible)
=> sinx = k - 2
sinx range = - 1 to 1
=> k = 1 to 3
k ∈ [1 , 3]
a + b = 1 + 3 = 4
(a + b) is equal to 4
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Step-by-step explanation:
please see the attachment here is your ans
