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Question

Number of values of x (x[0,π]) for which the equation 2sinx2cosx+cotx=1 holds good

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Solution


2sinx2cosx+cotx=1
2sinx2cosx+1tanx=1
2sinxtanx2sinxtanx+1=0
(2sinx1)(tanx1)=0
sinx=12 or tanx=1
x=π6,5π6 or π4

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