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If x=5,y=6,z=7.The value of sin^(2)((X+Y...

If x=5,y=6,z=7.The value of `sin^(2)((X+Y)/2)`, is

A

`3/5`

B

`4/5`

C

`2/5`

D

`1/5`

Text Solution

Verified by Experts

we obtain x = 5, y = 6, z = 7.
Now,
`sin^(2)((X+Y)/2)=sin^(2)((pi-Z)/2)=cos^(2)Z/2=1/2(1+cosZ)`
`=1/2+1/2((x^(2)+y^(2)-z^(2))/(2xy))=1/2+(25+36-49)/(4xx5xx6)=1/2+12/120=3/5`
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