Find the number of solutions of the equations; P (i) \( |\cot x|=\c...

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Find the number of solutions of the equations;
P
(i) \( |\cot x|=\cot x+\frac{1}{\sin x} \), when \( x \in[0,2 \pi] \)
(ii) \( \sin ^{3} x \cos x+\sin ^{2} x \cdot \cos ^{2} x+\sin x \cdot \cos ^{3} x=1 \), when \( x \in[0,2 \pi] \)
(iii) \( 2^{\cos x}=|\sin x| \), when \( x \in[-2 \pi, 2 \pi] \)
(iv) \( |\cos x|=[x] \), (where [.] denotes the greatest integer function).
(v) \( x+2 \tan x=\frac{\pi}{2} \), when \( x \in[0,2 \pi] \).
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