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If the equation 2ksinx + 7 = 4k – cos2x possesses a solution for K E [a, b], then (a + b) is equal to |
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Answer» equation 2ksinx + 7 = 4k – cos2x possesses a SOLUTION for k ∈ [a , b] To FIND : (a + b) valueSolution: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 - 2sinx range = - 1 to 1=> k = 1 to 3 k ∈ [1 , 3] a + b = 1 + 3 = 4(a + b) is equal to 4Learn More:brainly.in/question/27346284Solve the equation √3 sin x - cos x = √2 - Brainly.in brainly.in/question/2607997 |
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