If [ x ] denotes the greatest integer ≤ x , then the system of linear equations [ s i n θ ] x + [ - c o s θ ] y = 0 , [ c o t θ ] x + y = 0

Question

If [ x ] denotes the greatest integer ≤ x , then the system of linear equations [ s i n θ ] x + [ - c o s θ ] y = 0 , [ c o t θ ] x + y = 0, has a unique solution if θ ∈ π 2 , 2 π 3 ∪ π , 7 π 6, have infinitely many solution if θ ∈ π 2 , 2 π 3 ∪ π , 7 π 6, has a unique if θ ∈ π 2 , 2 π 3 and have infinitely many solutions if θ ∈ π , 7 π 6, have infinitely many solutions if θ ∈ π 2 , 2 π 3 and has a unique solution if θ ∈ π , 7 π 6

MARKS App · Accepted Answer

sin ⁡ θ x + - cos ⁡ θ y = 0 and cos ⁡ θ x + y = 0 for infinite many solution sin ⁡ θ - cos ⁡ θ cot ⁡ θ 1 = 0 i.e. sin θ = - cos θ c o t θ . . . i when θ ∈ π 2 , 2 π 3 then s i n θ ∈ 0 , 1 2 ⇒ sin θ = 0 and - cos θ ∈ 0 , 1 2 ⇒ - cos θ = 0 and cot θ ∈ - 1 3 , 0 ⇒ cot θ = - 1 When θ ∈ π , 7 π 6 then s i n θ ∈ - 1 2 , 0 ⇒ sin θ = - 1 and - cos θ ∈ 3 2 , 1 ⇒ - cos θ = 0 and cot θ ∈ 3 , ∞ ⇒ cot θ ∈ 2 , 3 , 4 , . . . ∞ When θ ∈ π 2 , 2 π 3 then the equation i satisfied therefore infinitely many solution. When θ ∈ π , 7 π 6 then the equation i not satisfied therefore unique solution.

Search any question & find its solution

Looking for more such questions to practice?