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Question
The number of ordered pairs (α,β), where α,β∈(−π,π) satisfying cos(α−β)=1 and cos(α+β)=1e is?
The number of ordered pairs (α,β), where α,β∈(−π,π) satisfying cos(α−β)=1 and cos(α+β)=1e is?
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Solution
The correct option is D 4
Cos(α+β)=1ecos(α−β)=1−π⩽α,β⩽πGraphofcosα(fig....1.1)ascos(α−β)=1α−β=0(ininterval−π⩽α,β⩽π)cos(α+β)=1ecos(2α)=1e−π⩽α⩽π−2π⩽2α⩽2πSodrawthegraphofcosα(fig....1.2)Sothevalueofαare4sothereare4orderedpairs
Cos(α+β)=1ecos(α−β)=1−π⩽α,β⩽πGraphofcosα(fig....1.1)ascos(α−β)=1α−β=0(ininterval−π⩽α,β⩽π)cos(α+β)=1ecos(2α)=1e−π⩽α⩽π−2π⩽2α⩽2πSodrawthegraphofcosα(fig....1.2)Sothevalueofαare4sothereare4orderedpairs
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