what is value of sin square x/2-cossquarex/2
Answers
Step-by-step explanation:
Lety=2sin2x+2cos2x
y=eln(2)sin2x+eln(2)cos2x
dydx=ln(2)eln(2)sin2x2sinxcosx−ln(2)eln(2)cos2x2sinxcosx
dydx=ln(2)sin2x(2sin2x−2cos2x)
For minimum value dydx should be 0.
0=ln(2)sin2x(2sin2x−2cos2x)
Case 1
2sin2x−2cos2x=0
2sin2x=2cos2x
sin2x=cos2x
sinx=±cosx
sinx±cosx=0
12–√sinx±12–√cosx=0
sin(x±π4)=0
x±π4=0,π
Thus x=−π4,π4,3π4,5π4
Putting these value of x in y we get
y=22–√
Case 2
sin2x=0
2x=0,π
x=0,π2
Putting these value of x in y we get
y=3
Thus ymin=22–√ and ymax=3
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