Let S be the set of all ∈R such that the equation, cos2x+ sinx=2 -7 has a solution. Then S is equal to :

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Accepted Answer

Correct answer: D. (d) JEE Main 2019 Given equation is, cos2x+ sinx=2 -7 1-2 sin^2x+ sinx=2 -7 2 sin^2x- sinx+(2 -8)=0 ⇒ sinx= ^2-8(2 -8)4=0 ⇒ sinx= ( -8)4 ⇒ sinx= -44( sinx=2 ( rejected )) ∵equation has solution, then -44 ∈(-1 ,1) ⇒ ∈ (2 ,6 )

$Let S be the set of all α \in R such that the equation, cos 2 x + α sin x = 2 α - 7 has a solution. Then S is equal to :$

Solution

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