Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Find the range of
f(x) = [sin x + 
] cos x
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. f(x) is defined ∀ x ∈ R
Let f(x) = y
∴ y = cos x. sin x + 
. Cosx
⇒ (y – cos x. sin x) 2 = cos 2 x (sin 2 x + sin 2 α )
⇒ y 2 – 2y cos x sin x – cos 2 x. sin 2 α = 0
⇒ y 2 (1+ tan 2 x) –2y tan x – sin 2 α = 0
(dividing y cos 2 x)
⇒ y 2 tan 2 x –2y tan x + (y 2 –sin 2 α) = 0
tan x ∈ R ⇒ Descriminant ≥ 0
⇒ 4y 2 –4y 2 (y 2 – sin 2 α ) ≥ 0
⇒ y 2 – (1 + sin 2 α ) ≤ 0
⇒ – 
≤ y ≤ 
Hence Range is [– 
, 
]
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