The set of values of a for which the equation √acosx−2sinx=√2+√2−a possesses a solution, is
A
[−1−√5,−1+√5]
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B
[√5−1,2]
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C
R
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D
(−∞,−1−√5)
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Solution
The correct option is B[√5−1,2] Clearly, a≥0 and 2−a≥0 ⇒0≤a≤2⋯(1) Now, for solution to exist, √2+√2−a≤√a+4⇒2+2−a+2√2√2−a≤a+4⇒√2√2−a≤a⇒2(2−a)≤a2⇒a2+2a−4≥0 ⇒a≤−1−√5 or a≥−1+√5⋯(2) From (1) and (2), √5−1≤a≤2