If [ 2 cos x ] + [ sin x ] = − 3, then the range of the function, f (x) = sin x + 
cos x in [0, 2 π ] lies in (where [ . ] denotes greatest integer function)
, 
)
]
)
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(b,c,d)[2 cos x] + [sin x] = – 3
–2 ≤ 2 cos x ≤ 2 ⇒ [2 cos x] = 2, 1, –1, –2
– 1 ≤ sin x ≤ 1 ⇒ [sin x] = 1, 0, –1
Equation holds true for [2 cos x] = – 2 and [sin x] = –1
⇒ – 1 ≤ cos x < – 
and – 1 ≤ sin x < 0
⇒ x ∈ 
and x ∈ ( π , 2 π ) ⇒ x ∈ 
f(x) = sin x + 
cos x
f(x) = 2 sin 
< x + 
< 
⇒ – 1 ≤ sin 
< – 
⇒ – 2 ≤ 2 sin 
< – 
Hence range is 
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