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The number of integers in the range of 3...

The number of integers in the range of `3 sin^(2)x+3sin x cos x+7cos^(2)x` is

A

3

B

4

C

5

D

6

Text Solution

Verified by Experts

The correct Answer is:
C
`3 sin^(2)x+3 sin x.cos x+7 cos^(2)x`
`=(3(1-cos 2x))/(2)+(3sin 2x)/(2)+(7(1+cos 2x))/(2)`
`=(3 sin 2x 2x + 4 cos 2x)/(2)+5`
Now `-5 le 3 sin 2x + 4 cos 2x le 5`
`therefore (3 sin 2x + 4 cos 2x)/(2)+5 in [(5)/(2),(15)/(2)]`
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