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Biggest among (sin1+cos1),(sqrt(sin1))...

Biggest among
`(sin1+cos1),(sqrt(sin1))+sqrt(cos1)),sqrt(1+sin2)and 1, is`

A

`sin1 +cos1`

B

`sqrt(sin1)+sqrt(cos1)`

C

`sqrt(1+sin2)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`sqrt(sin1)gtsin1gtsin^(2)1 and, sqrt(cos1)gtcos1 gtcos^(2)1`
`thereforesqrt(sin)1+sqrt(cos1)gtsin1+cos+gt1`
`Also, sqrt(1+sin2)=sqrt(sin^(2)1+cos^(2)1+2 sin1 cos1)=sin1+cos1`
`thereforesqrt(sin1)+sqrt(cos1)gtsqrt(1+sin2)gt1.`
Hence, ` sqrt(sin1)+sqrt(cos1)` is the greatest.
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