In ` A B C ,s i d e sb , c` and angle `B` are given such that `a` has two valus `a_1a n da_2dot` Then prove that `|a_1-a_2|=2sqrt(b^2-c^2sin^2B)`
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`cos B = (c^(2) + a^(2) - b^(2))/(2ca)`
or `a^(2) - (2c cos B) a + c^(2) - b^(2) = 0`
This equation has roots `a_(1) and a_(2)`
`rArr a_(1) + a_(2) = 2c cos B, a_(1) a_(2) = c^(2) - b^(2)`
`rArr (a_(1) -a_(2))^(2) = (a_(1) + a_(2))^(2) - 4a_(1) a_(2) = 4c^(2) cos^(2) B - 4(c^(2) - b^(2))`
`= 4b^(2) - 4c^(2) sin^(2) B = 4(b^(2) -c^(2) sin^(2) B)`
or `|a_(1) -a_(2)| = 2 sqrt(b^(2) - c^(2) sin^(2) B)`
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If `S=[((sqrt(3)-1)/(2sqrt(2)),(sqrt(3)+1)/(2sqrt(2))),(-((sqrt(3)+1)/(2sqrt(2))),(sqrt(3)-1)/(2sqrt(2)))], A=[(1,0),(-1,1)]` and `P=S ("adj.A") S^(T)
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Here, `tan^(_1) ((a_(1) x- y)/(a + a_(1) y)) = tan^(-1) ((a_(1) - (y)/(x))/(1 + a_(1) (y)/(x))) = tan^(-1) a_(1) - tan^(-1) (y)/(x)` `tan^(-1) ((a_(2) -a_(1))/(1 + a_(2) a_(1))) = tan^(-1)...
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For natural numbers `m`, `n`, if `(1-y)^m(1+y)^n=1+a_1y+a_2y^2+...,` and `a_1=a_2=10` then (A)`mltn` (B)`mgtn` (C)`m+n=80` (D)`m-n=20`
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If `p` is the probability that a man aged `x` will die in a year, then the probability that out of `n` men `A_1,A_2, A_n` each aged `x ,A_1` will die
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