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  • If [x] denotes the greatest integer not exceeding the real number x , then the number of solutions of the equation cos x + [ sin x ] , in the interval [0,2pi] is

If [x] denotes the greatest integer not exceeding the real number x , then the number of solutions of the equation cos x + [ sin x ] , in the interval [0,2pi] is

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Solution:      [sin x] ightarrow R(f)=�,-1,1

               Now ,    cosx=1Rightarrow x=0,pi

              Similarly ,    cos x=0Rightarrow x=fracpi2,frac3pi2.

            But these values  do not satisfy the given equation .

             Therefore , the number of solutions is nil.

Posted by

Deependra Verma

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