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SHIVLAAL PUBLICATION-सारणिक-सिद्ध कीजिए कि:
- |(1,x,y),(0,cosx,siny),(0,sinx,cosy)|=cos(x+y)
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- |(0,1,sec alpha),(tan alpha, -sec alpha, tan alpha),(1,0,1)|=sec^(2)al...
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- |(x,y,z),(-x,y,z)|=4xyz.
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- |(1+x,y,z),(x,1+y,z),(x,y,1+z)|=1+x+y+z
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- |(x,1,1),(1,x,1),(1,1,x)|=(x+2)(x-1)^(2)
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- |(1+x,1,1),(1,1+x,1),(1,1,1+x)|=x^(2)(x+3)
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- |(1,1,1),(1,1+x,1),(1,1,1+y)|=xy
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- |(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b))|=0
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- [(a-b,b-c,c-a),(b-c,c-a,b-c),(c-a,a-b,b-c)]=0
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- सिद्ध करें कि |(a+b,a+2b,a+3b),(a+2b,a+3b,a+4b),(a+4b,a+5b,a+6b)|=0
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- |(1,a,b),(-a,1,c),(-b,-c,1)|=1+a^(2)+b^(2)+c^(2)
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- |(a,b,c),(b,c,a),(c,a,b)|=3abc-a^(3)-b^(3)-c^(3)
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- |(b+c,a+b,a),(c+a,b+c,b),(a+b,c+a,c)|=a^(3)+b^(3)+c^(3)-3abc
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- |(a,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)|=a^(3)+b^(3)+c^(3)-3abc
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- सिद्ध कीजिए कि: |(b-c,c-a,a-b),(c,a,b),(1,1,1)|=(a-b)(b-c)-(c-a)^(2)
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- |(1,a,bc),(1,b,ca),(1,c,ab)|=(a-b)(b-c)(c-a)
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- |(b+c,a,b),(c+a,c,a),(a+b,b,c)|=(a+b+c)(a-c)^(2)
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- |((a^(2)+b^(2))/c,c,c),(a,(b^(2)+c^(2))/a,a),(b,b,(c^(2)+a^(2))/b)|=4a...
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- |(0,ab^(2),ac^(2)),(a^(2)b,0,bc^(2)),(a^(2)c,b^(2)c,0)|=2a^(3)b^(3)c^(...
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- |(a^(2),2ab,b^(2)),(b^(2),a^(2),2ab),(2ab,b^(2),a^(2))|=(a^(3)+b^(3))^...
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