Trigonometric EquationMedium
Question
The set of equations (cosθ)x + (sinθ)y = 1
(secθ)x - (sinθ)y = cos2q
(sinθ)x - (cos3θ)y = cosθ sin3θ
(secθ)x - (sinθ)y = cos2q
(sinθ)x - (cos3θ)y = cosθ sin3θ
Options
A.is consistent for all values of θ
B.is consistent for all values of θ except when θ is odd multiple of 
C.has a unique solution
D.has infinite number of solutions
Solution
(cosθ)x + (sinθ)y = 1 .... (i)
(secθ)x - (sinθ)y = cos2θ .... (ii)
(sinθ)x - (cos3θ)y = cosθ sin3θ .... (iii)
(1) satisfied by x = cosθ, y = sin θ
This values also satisfies other.
⇒ set of equation is consistent for all θ
except when θ is odd multiple of
(secθ)x - (sinθ)y = cos2θ .... (ii)
(sinθ)x - (cos3θ)y = cosθ sin3θ .... (iii)
(1) satisfied by x = cosθ, y = sin θ
This values also satisfies other.
⇒ set of equation is consistent for all θ
except when θ is odd multiple of
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