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brilliants [131]
3 years ago
10

Find all solutions in the interval [0,2π) of the equation.

Mathematics
1 answer:
Sauron [17]3 years ago
3 0

Step-by-step explanation:

2sin(x)cos(x) - sin(x) + 2cos(x)-1= 0

<=> sinx( 2cosx -1) + ( 2cosx -1) =0

<=> (sinx +1) + ( 2cosx-1)=0

<=> sinx=-1 or cosx= 1/2

+) sinx=1 => x= pi/2 + k×2pi

+)cosx=1/2 => x= pi/3+ k×2pi or x=-pi/3 + k×2pi

x€ [0,2pi] => x= pi/2, pi/3.

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