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If x in (pi,(3pi)/2),t h e n4cos^2(pi/4-...

If `x in (pi,(3pi)/2),t h e n4cos^2(pi/4-x/2)+sqrt(4sin^4x+sin^2 2x)` is always equal to 1 (b) 2 (c) `-2` (d) none of these

A

1

B

2

C

`-2`

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
B
`4cos^(2)((pi)/(4)-(x)/(2))+sqrt(4sin^(4)x+sin^(2)2x)`
`=4cos^(2)((pi)/(4)-(x)/(2))+sqrt(4sin^(2)x(cos^(2)x+sin^(2)x))`
`=2(1+cos((pi)/(2)-x))+2|sinx|`
`=2+2sinx-2sinx` [as `x in(pi,(3pi)/(2)`)]
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