Published by:
CGP EDU Academic Team
Published on: August 12, 2026
The equation sin 6 x + cos 6 x = a 2 has real solution if
A
a ∈ (–1, 1)
B
a ∈ 
C
a ∈ 
D
a ∈ 
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(b,d)
sin 6 x + cos 6 x = a 2 ⇒ (sin 2 x + cos 2 x) (sin 4 x + cos 4 x – sin 2 x cos 2 x) = a 2
⇒ (sin 2 x + cos 2 x) 2 – 3sin 2 x cos 2 x = a 2 ⇒ 1 – 3 sin 2 x cos 2 x = a 2
⇒ 1 – 
sin 2 2x = a 2 ⇒ 
= sin 2 2x
⇒ 0 ≤ 
(1 – a 2 ) ≤ 1
1 – a 2 ≥ 0 and 4 – 4a 2 ≤ 3
a 2 ≤ 1 and 
≤ a 2
– 1 ≤ a ≤ 1 and a ≥ 
or a ≤ – 
a ∈ 
∪ 
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