The solution of the equation (sinx+cosx)1+sin2x=2,−π≤x≤π, is
A
π2
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B
π
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C
π4
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D
none of these
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Solution
The correct option is Cπ4 (cosx+sinx)1+sin2x=2 ⇒(cosx+sinx)(cosx+sinx)2=2 ⇒1√2cosx+1√2sinx=±1 ⇒cos(x−π4)=±1 hence solution in the given interval is, x=−3π4,π4 Hence, option 'C' is correct.