Trigonometric EquationHard
Question
If system of equations x + 2y + 3z = 2, 2x + 3y – (2sinθ)z = 9 and 3x + 5y + 2z = √3 sec θ + 9 haveinfinite solutions, then number of values of θ in the interval [0, 2π] is -
Options
A.0
B.1
C.2
D.4
Solution
For infinite solutions D = Dx = Dy = Dz = 0 & No two planes are parallel
D =
= 0 ⇒ sin θ = 
two possibilities θ = 30º, 150º
So secθ is either
or -
For secθ = -
Dx
(Dx≠ 0)
for sec θ = , Dx = Dy = Dz = 0
& No two planes are parallel hence only 1 value.
D =
= 0 ⇒ sin θ = two possibilities θ = 30º, 150º
So secθ is either
or - For secθ = -
Dx
(Dx≠ 0) for sec θ =
, Dx = Dy = Dz = 0& No two planes are parallel hence only 1 value.
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