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If A=75^0,b=45^0, then prove that b+csqr...

If `A=75^0,b=45^0,` then prove that `b+csqrt(2)=2a`

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`A = 75^(@) , B = 45^(@) rArr C = 60^(@)`
Now, `(a)/(sin A) = (b)/(sin B) = (c)/(sin C) = 2R`
`rArr b + c sqrt2 = (sin 45^(@))/(sin 75^(@)) a + sqrt2 (sin 60^(@))/(sin 75^(@)) a`
`((1)/(sqrt2))/((sqrt3 + 1)/(2 sqrt2)) a + sqrt2 ((sqrt3)/(2))/((sqrt3 + 1)/(2 sqrt2)) a`
`= (2)/(sqrt3 + 1) a + (2 sqrt3 a)/(sqrt3 + 1) = 2a`
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