JEE Main 2024 Mathematics question
Not in JEE Main syllabus
Let the set of all a ∈ R such that the equation cos2x + a sinx = 2a – 7 has a solution be [p, q] and r = tan9° – tan27° – + tan81°, then pqr is equal to .
Answer: 48
Solution
With t = sin x: 2t² − at + 2a − 8 = 0, i.e. (t − 2)(2t + 4 − a) = 0, so a = 2 sin x + 4 ∈ [2, 6]. Hence p = 2,
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