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

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

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Given determinant = `cos^2 theta + sin^2 theta = 1`
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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 .

A N EXCEL PUBLICATION-DETERMINANTS-QUESTION TYPE
  1. Evaluate |[cos theta, -sin theta], [sin theta, cos theta]|

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

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  3. Evaluate |[1,1,1],[a,b,c],[b+c,c+a,a+b]|

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

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

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

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  7. Using properties, prove that |[1,omega,omega^2],[omega,omega^2,1],[om...

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  8. Without expanding the determinant prove the following. |[a-b,b-c,c-a...

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

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  10. Consider the determinant D=|[1,3,5],[2,6,10],[31,11,38]| On taking 2 ...

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  11. Consider the determinant D=|[1,3,5],[2,6,10],[31,11,38]| Evaluate De...

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  12. Consider the determinant Delta =|[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-b...

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  13. Consider the determinant Delta =|[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-b...

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  14. Consider the equation |[3x-8,3,3],[3,3x-8,3],[3,3,3x-8]|=0 OperatingC1...

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  15. Consider the equation |[3x-8,3,3],[3,3x-8,3],[3,3,3x-8]|=0 Solve the ...

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  16. Without expanding the determinant prove the following. |[x,a,x+a],[y...

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  17. Without expanding the determinant prove the following. |[2,7,65],[3,...

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  18. Without expanding the determinant prove the following. |[b+c,q+r,y+z...

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  19. Without expanding the determinant prove the following. |[1,bc,a(b+c)...

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  20. Without expanding the determinant prove the following. |[a-b,b-c,c-a...

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  21. By using properties of determinants, prove that |[0,a ,-b],[-a,0,-c],...

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