Trigonometric EquationHard
Question
The number of all possible triplets (a1 ,a2 ,a3) such that a1 + a2 cos(2x) + a3 sin(x) = 0 for all x is
Options
A.0
B.1
C.3
D.∞
Solution
Given, α1 + α2 cos 2x + α3 sin2 x = 0, for all x
⇒ α1 + α2 cos 2x + α3
= 0, for all x
⇒
cos 2x = 0, for all xc
⇒
and 
⇒
, where k ∈ R
Hence, the solutions, are
, where k is any real number.
Thus, the number of triplets is infinite.
⇒ α1 + α2 cos 2x + α3
= 0, for all x⇒
cos 2x = 0, for all xc⇒
and ⇒
, where k ∈ RHence, the solutions, are
, where k is any real number.Thus, the number of triplets is infinite.
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