If alpha,beta,gamma are real numbers,...

If `alpha,beta,gamma` are real numbers, then without expanding at any stage, show that `|1cos(beta-alpha)"cos"(gamma-alpha)"cos"(alpha-beta)1"cos"(gamma-beta)"cos"(alpha-gamma)"cos"(beta-gamma)1|=0`

`4 cos alpha cos beta cos gamma`

`2 cos alpha cos beta cos gamma`

`4 sin alpha sin beta sin gamma`

none of these

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|[1,cos(alpha-beta), cos alpha] , [cos(alpha-beta),1,cos beta] , [cos alpha, cos beta, 1]|

OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise

Prove the identities: |{:(b^(2)+c^(2),,ab,,ac),(ab,,c^(2)+a^(2),,bc),...
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a^(−1)+b^(−1)+c^(−1)=0 such that |[1+a,1,1,],[1,1+b,1,],[1,1,1+c,]| =△...
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If alpha,beta,gamma are real numbers, then without expanding at any...
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If A,B,C are the angles of triangle ABC, then the minimum value of |{:...
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If x, y , z are in A.P., then the value of the det (A) is , where A ...
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Find the number of real root of the equation |0x-a x-b x+a0x-c x+b x+c...
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If a , b , c are distinct, then the value of x satisfying |0x^2-a x^3-...
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Let the following system of equations {:(kx+y+z=1),(x+ky+z=k),(x+y+k...
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Show that: |b^2+c^2a b a c b a c^2+a^2b c c a c b a^2+b^2|=4a^2b^2c^2
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Let triangle =|[2a1b1, a1b2+a2b1, a1b3+a3b1], [a1b2+a2b1, 2a2b2, a2b3+...
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If B is a non-sinfular matrix and A is square matrix, then det B^(-1)A...
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If 0 lt theta lt pi and the system of equations (sin theta) x + y + ...
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If the determinant |(b -c,c -a,a -b),(b' -c',c' -a',a' -b'),(b'' -c'',...
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If a !=b, then the system of equation ax + by + bz = 0 bx + ay + bz ...
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if |{:(1,,1,,1),(a,,b,,c),(a^(3),,b^(3),,c^(3)):}|= (a-b)(b-c)(c-a)(a+...
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Show that a x+b y+r=0,b y+c z+p=0a n dc z+a x+q=0 are perpendicular to...
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Consider the function f(x) = |{:(a^(2)+x,,ab,,ac),(ab,,b^(2)+x,,bc),(a...
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The equation |(x-a,x-b,x-c),(x-b,x-a,x-c),(x-c,x-b,x-a)|=0 (a,b,c are ...
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Let A = [(1,sin theta,1),(- sin theta,1,sin theta),(-1,-sin theta,1)],...
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If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab...
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