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Find the max and min value of cos*(45+x)+(sinx-cosx)* (*means square)
Find the max and min value of cos*(45+x)+(sinx-cosx)*                  (*means square)

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4 years ago

```							 cos*(45+x)+(sinx-cosx)*open the square ones,=>  cos*(45+x)+((sinx)* + (cosx)* -2sinxcosx)=>  cos*(45+x) + 1 – sin2xnow, maximum value for cos^2x is 1. and minimum zero.and sin2x would have -1 when cos^2x is 1 and 1 when cos^2x is 0.Because sinx and cos cannot have maximum and minimum value simulataneously .
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4 years ago
```							The maximum value of the function is 3 and minimum vaues is 0 as proved below.using formula for cos2x and expanding the bracket the expression becomes1/2[cos(pie/2 + 2x) + 1] + 1 – 2sinxcosx= 1/2[-sin2x + 1]  + 1 -sin2x= 3/2 -3/2sin2xThe maximum value is when sin2x = -1max value = 3/2+ 3/2 = 3.The mimimum value is when sin2x = 1min value =3/2-3/2 = 0
```
4 years ago
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