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Q.

If y=(sin⁡x+cosec⁡x)2+(cos⁡x+sec⁡x)2  then the minimum value of y, ∀x∈R is

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a

7

b

3

c

9

d

0

answer is C.

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Detailed Solution

y=sin2⁡x+cos2⁡x+2(sin⁡xcosec⁡x+cos⁡xsec⁡x)+sec2⁡x+cosec2⁡x=5+2+tan2⁡x+cot2⁡x=7+(tan⁡x−cot⁡x)2+2∴ ymin=9
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If y=(sin⁡x+cosec⁡x)2+(cos⁡x+sec⁡x)2  then the minimum value of y, ∀x∈R is