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The general solution of the equation sin x + cos x = 2 is
- a)nπ,n∈I
- b)2nπ+π/ 2or 2nπ,n∈I
- c)2n2π+π/2 or 2nπ,n∈I
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The general solution of the equation sin x + cos x = 2 isa)nπ,n&isi...
sinx+cosx=2—(1)sinx+cosx=2—(1)
Divide by 2–√2on both LHSandRHS=>sinx∗12√+cosx∗12√=22√=2–√—(2)LHSandRHS=>sinx∗12+cosx∗12=22=2—(2)
Since sin45=cos45=12√sin45=cos45=12, the equation(2)(2) can be written assinxcos45+cosxsin45=2–√—(3)sinxcos45+cosxsin45=2—(3)
SincesinAcosB+cosAsinB=sin(A+B)sinAcosB+cosAsinB=sin(A+B), equation (3)(3)can be written as sin(x+45)=2–√—(4)sin(x+45)=2—(4)
The known facts are:
- The value for sinAsinAis always between−1−1and11
- 2–√=1.4142=1.414, which is greater than 1
From the above facts, LHS of the equation (4) is always between -1 and 1 whereas RHS is > 1. This is not possible and hence six+cosxsix+cosx can never be equal to 2.
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The general solution of the equation sin x + cos x = 2 isa)nπ,n∈Ib)2nπ+π/ 2or 2nπ,n∈Ic)2n2π+π/2 or 2nπ,n∈Id)none of theseCorrect answer is option 'D'. Can you explain this answer?
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The general solution of the equation sin x + cos x = 2 isa)nπ,n∈Ib)2nπ+π/ 2or 2nπ,n∈Ic)2n2π+π/2 or 2nπ,n∈Id)none of theseCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The general solution of the equation sin x + cos x = 2 isa)nπ,n∈Ib)2nπ+π/ 2or 2nπ,n∈Ic)2n2π+π/2 or 2nπ,n∈Id)none of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The general solution of the equation sin x + cos x = 2 isa)nπ,n∈Ib)2nπ+π/ 2or 2nπ,n∈Ic)2n2π+π/2 or 2nπ,n∈Id)none of theseCorrect answer is option 'D'. Can you explain this answer?.
The general solution of the equation sin x + cos x = 2 isa)nπ,n∈Ib)2nπ+π/ 2or 2nπ,n∈Ic)2n2π+π/2 or 2nπ,n∈Id)none of theseCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The general solution of the equation sin x + cos x = 2 isa)nπ,n∈Ib)2nπ+π/ 2or 2nπ,n∈Ic)2n2π+π/2 or 2nπ,n∈Id)none of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The general solution of the equation sin x + cos x = 2 isa)nπ,n∈Ib)2nπ+π/ 2or 2nπ,n∈Ic)2n2π+π/2 or 2nπ,n∈Id)none of theseCorrect answer is option 'D'. Can you explain this answer?.
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