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Evaluate |[cos theta, -sin theta], [sin ...

Evaluate `|[cos theta, -sin theta], [sin theta, cos theta]|`

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If A=[[cos theta, sin theta],[ -sin theta, cos theta]] , then prove that A^n=[[cos ntheta, sinn theta],[ -sin n theta, cos n theta]] , n in N .

Show that [[1 , -tan theta ],[ tan theta, 1]][[1, tan theta],[ -tan theta, 1]]^(-1)=[[cos 2 theta, -sin 2 theta],[ sin 2 theta, cos 2 theta]]

If A=[[costheta,sintheta],[-sintheta,costheta]] then prove that A^2=[[cos2theta,sin2theta],[-sin2theta,cos2theta]]

The product of matrices A = [(cos^(2) theta, cos theta sin theta),(cos theta sin theta , sin^(2) theta)] and sin B = [(cos^(2)phi, cos phi sin phi),(cos phi sin phi, sin^(2) phi)] is a null matrix if theta - phi =

If x and y are connected parametrically by the equation without eliminating the parameter, find (dy/dx) if x=a(cos theta+theta sin theta) y=a(sin theta-theta cos theta)

If a cos theta+b sin theta=c , show that asin theta-bcos theta=pm sqrt((a)^(2)+(b)^(2)-(c)^(2))

(b)Show that (sin theta+sin 3theta+sin 5 theta+sin 7 theta)/(cos theta+cos3theta+cos 5 theta+cos 7 theta)=tan 4 theta .

If cos theta =7/25 and theta is an angle in the fourth quadrant, find the value of (25 cos theta -7 tan theta)/(cos theta-sin theta) .

Solve sqrt 2+sin theta=cos theta .

V PUBLICATION-DETERMINANT-QUESTION BANK
  1. Find the values of x in which abs[[3,x],[x,1]]=abs[[3,2],[4,1]]

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  2. Evaluate |[2,4],[-5,-1]|

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  3. Evaluate |[cos theta, -sin theta], [sin theta, cos theta]|

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  4. If A = [[1,2],[4,2]] then show that |2A|= 4|A|

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  5. If A=[[1, 0, 1],[ 0, 1, 2],[ 0, 0, 4]] then show that |3 A|=27...

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  6. Evaluate the determinants (i) |[3 , -1, -2],[ 0, 0, -1],[ 3, -5,...

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  7. If A = [(1,1,-2),(2,1,-3),(5,4,-9)]. Find |A|

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  8. Find values of x if i) |[2 , 4],[ 5, 1]|=|[2 x, 4], [6, x]| ii) ...

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  9. If |[x ,2],[ 18, x]|=|[ 6, 2 ],[ 18, 6]|, then x is equal to a)6 ...

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  10. Verify Property 1 for Delta=|[2 ,-3, 5],[ 6, 0, 4],[ 1, 5, -7]...

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  11. Verify Property 2 for Delta=|[2 , -3, 5],[ 6, 0, 4],[ 1, 5, -7]...

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  12. Evaluate Delta=|[3, 2, 3],[ 2, 2, 3],[ 3, 2, 3]|

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  13. Evaluate |[102, 18, 36],[ 1, 3, 4],[ 17, 3, 6]|

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  14. prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0

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  15. Prove that |[a, a+b, a+b+c],[ 2 a, 3 a+2 b, 4 a+3 b+2 c],[ 3 a, ...

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  16. Without expanding prove that abs[[x+y,y+z,z+x],[z,x,y],[1,1,1]]=0

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  17. Evaluate Delta=|[1, a, bc],[ 1, b, c a],[ 1, c, a b]|

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  18. Using properties of determinants prove the following. abs[[b+c,a,...

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  19. Consider the determinant Delta=abs[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,...

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  20. Using properties of determinants show that abs[[1+a,1,1],[1,1+b,1]...

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