मराठी

Using Properties of Determinants, Prove That|(Sin Alpha, Cos Alpha, Cos(Alpha+ Delta)),(Sin Beta, Cos Beta, Cos (Beta + Delta)),(Sin Gamma, Cos Gamma, Cos (Gamma+ Delta))| = 0 - Mathematics

Advertisements
Advertisements

प्रश्न

Using properties of determinants, prove that

`|(sin alpha, cos alpha, cos(alpha+ delta)),(sin beta, cos beta, cos (beta + delta)),(sin gamma, cos gamma, cos (gamma+ delta))| = 0`

Advertisements

उत्तर

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Determinants - Exercise 4.7 [पृष्ठ १४२]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 4 Determinants
Exercise 4.7 | Q 15 | पृष्ठ १४२

संबंधित प्रश्‍न

Using the properties of determinants, prove the following:

`|[1,x,x+1],[2x,x(x-1),x(x+1)],[3x(1-x),x(x-1)(x-2),x(x+1)(x-1)]|=6x^2(1-x^2)`


Using the property of determinants and without expanding, prove that:

`|(b+c, q+r, y+z),(c+a, r+p, z +x),(a+b, p+q, x + y )| = 2|(a,p,x),(b,q,y),(c, r,z)|`


By using properties of determinants, show that:

`|(y+k,y, y),(y, y+k, y),(y, y, y+k)| = k^2(3y + k)`


Evaluate `|(x, y, x+y),(y, x+y, x),(x+y, x, y)|`


Using properties of determinants, prove that:

`|(x, x^2, 1+px^3),(y, y^2, 1+py^3),(z, z^2, 1+pz^2)|` = (1 + pxyz) (x – y) (y – z) (z – x), where p is any scalar.


Using propertiesof determinants prove that:
`|(x , x(x^2), x+1), (y, y(y^2 + 1), y+1),( z, z(z^2 + 1) , z+1) | = (x-y) (y - z)(z - x)(x + y+ z)`


Using properties of determinants, prove the following:

`|(a, b,c),(a-b, b-c, c-a),(b+c, c+a, a+b)| = a^3 + b^3 + c^3 - 3abc`.


Evaluate the following determinants:

`|(x - 1, x, x - 2),(0, x - 2, x - 3),(0, 0, x - 3)| = 0`


Using properties of determinants, show that `|("a" + "b", "a", "b"),("a", "a" + "c", "c"),("b", "c", "b" + "c")|` = 4abc.


Solve the following equation: `|(x + 2, x + 6, x - 1),(x + 6, x - 1,x + 2),(x - 1, x + 2, x + 6)|` =  0


Without expanding the determinants, show that `|(x"a", y"b", z"c"),("a"^2, "b"^2, "c"^2),(1, 1, 1)| = |(x, y, z),("a", "b", "c"),("bc", "ca", "ab")|`


Without expanding the determinants, show that `|(0, "a", "b"),(-"a", 0, "c"),(-"b", -"c", 0)|` = 0


Without expanding determinants show that

`|(1, 3, 6),(6, 1, 4),(3, 7, 12)| + 4|(2, 3, 3),(2, 1, 2),(1, 7, 6)| = 10|(1, 2, 1),(3, 1, 7),(3, 2, 6)|`


Select the correct option from the given alternatives:

Let D = `|(sintheta*cosphi, sintheta*sinphi, costheta),(costheta*cosphi, costheta*sinphi, -sintheta),(-sintheta*sinphi, sintheta*cosphi, 0)|` then


Answer the following question:

Without expanding determinant show that

`|(l, "m", "n"),("e", "d", "f"),("u", "v", "w")| = |("n", "f", "w"),(l, "e", "u"),("m", "d", "v")|`


The value of `|(1, 1, 1),(""^"n""C"_1, ""^("n" + 2)"C"_1, ""^("n" + 4)"C"_1),(""^"n""C"_2, ""^("n" + 2)"C"_2, ""^("n" + 4)"C"_2)|` is 8.


Prove that: `|(y + z, z, y),(z, z + x, x),(y, x, x + y)|` = 4xyz


If A, B and C are angles of a triangle, then the determinant `|(-1, cos"C", cos"B"),(cos"C", -1, cos"A"),(cos"B", cos"A", -1)|` is equal to ______.


The maximum value of Δ = `|(1, 1, 1),(1, 1 + sin theta, 1),(1 + cos theta, 1, 1)|` is ______. (θ is real number)


If cos2θ = 0, then `|(0, costheta, sin theta),(cos theta, sin theta,0),(sin theta, 0, cos theta)|^2` = ______.


If the value of a third order determinant is 12, then the value of the determinant formed by replacing each element by its co-factor will be 144.


The determinant `|(sin"A", cos"A", sin"A" + cos"B"),(sin"B", cos"A", sin"B" + cos"B"),(sin"C", cos"A", sin"C" + cos"B")|` is equal to zero.


If the determinant `|(x + "a", "p" + "u", "l" + "f"),("y" + "b", "q" + "v", "m" + "g"),("z" + "c", "r" + "w", "n" + "h")|` splits into exactly K determinants of order 3, each element of which contains only one term, then the value of K is 8.


If a, b, c are the roots of the equation x3 - 3x2 + 3x + 7 = 0, then the value of `abs((2 "bc - a"^2, "c"^2, "b"^2),("c"^2, 2 "ac - b"^2, "a"^2),("b"^2, "a"^2, 2 "ab - c"^2))` is ____________.


`abs(("x", -7),("x", 5"x" + 1))`


Using properties of determinants `abs ((1, "a", "a"^2 - "bc"),(1, "b", "b"^2 - "ca"),(1, "c", "c"^2 - "ab")) =` ____________.


Without expanding determinants find the value of `|(10,57,107), (12, 64, 124), (15, 78, 153)|`


By using properties of determinant prove that `|(x + y, y+z, z +x),(z,x,y),(1,1,1)| =0`


By using properties of determinant prove that

`|(x+ y,y+z, z+x ),(z, x,y),(1,1,1)|` = 0 


Without expanding determinants find the value of `|(10, 57, 107),(12, 64, 124),(15, 78, 153)|`


Evaluate the following determinant without expanding:

`|(5, 5, 5),(a, b, c),(b + c, c + a, a + b)|`


By using properties of determinant prove that `|(x+y,y+z,z+x),(z,x,y),(1,1,1)|` = 0.


By using properties of determinant prove that

`|(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0`


Without expanding determinant find the value of `|(10,57,107),(12,64,124),(15,78,153)|`


By using properties of determinants, prove that 

`|(x+y, y+z, z+x),(z, x, y),(1, 1, 1)|` = 0 


By using properties of determinant prove that `|(x+y,y+z,z+x),(z,x,y),(1,1,1)|` = 0


By using properties of determinant prove that `|(x+y,y+z,z+x),(z,x,y),(1,1,1)|` = 0.


Without expanding evaluate the following determinant.

`|(1, a, b + c),(1, b, c + a),(1, c, a + b)|`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×