# 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

Solution:      $[\sin x]\rightarrow R(f)=\{0,-1,1\}$

Now ,    $cosx=1\Rightarrow x=0,\pi$

Similarly ,    $\cos x=0\Rightarrow x=\frac{\pi}{2},\frac{3\pi}{2}.$

But these values  do not satisfy the given equation .

Therefore , the number of solutions is nil.

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