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Sin2x - 2cosx+4sinx=4 in interval (0,5pie). Aieee question fast answer with solution

Abhinav , 7 Years ago
Grade 11
anser 1 Answers
Hrishikesh Datta

Last Activity: 7 Years ago

sin2x-2cosx+4sinx=4
2sinxcosx+4sinx=4+2cosx
2sinx(2+cosx)=2(2+cosx)
2sinx(2+cosx)-2(2+cosx)=0
(2+cosx)(2sinx-2)=0
now,
 2+cosx=0 and 2sinx-2=0
cosx=-2(which is not possible).
2sinx=2
sinx=1.
Now if we draw the graph of sinx=1 between 0 to 5 Pi, we will see that it intersects at 3 points.
Thus number of solutions will be 3.
 

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