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Prove that the determinant |[x,sintheta,...

Prove that the determinant `|[x,sintheta,costheta],[-sintheta,-x,1],[costheta,1,x]|`, is independent of `theta`

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Evaluate the determinant: |[costheta,-sintheta],[sintheta,costheta]|

Prove that (sectheta+tantheta)(1-sintheta)=costheta .

Prove that sin^3theta+cos^3theta=(sintheta+costheta)(1-sinthetacostheta) .

Prove that sintheta(cosectheta-sintheta)=cos^2theta .

Prove that sintheta/(1+costheta)+sintheta/(1-costheta)=2/sintheta .

Evaluate |(2costheta,-2sintheta),(sintheta,costheta)|

Write the inverse of the matrix: {:[(costheta, sintheta),(-sintheta,costheta)]

Prove that (sintheta-2sin^3theta)/(2cos^3theta-costheta)=tantheta .

Prove that (1-sintheta)/(1+sintheta)=(sectheta-tantheta)^2 .

PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. If |(3x,7),(-2,3)| = |(8,7),(-2,3)| find x.

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  2. Find x if det A = 0 where A = [(x+1,-3,4),(-5,x+2,2),(4,1,x-6)]

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  3. Prove that the determinant |[x,sintheta,costheta],[-sintheta,-x,1],[co...

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  4. Evaluate the following determinants: |(1,3,9),(3,9,1),(9,1,3)|

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  5. Evaluate the following determinants: |(2,3,7),(13,17,5),(15,20,12)|

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  6. Evaluate the following determinants: |(102,18,36),(1,3,4),(17,3,6)|

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  7. Evaluate the following determinants: |(1,-3,3),(4,-1,3),(3,5,3)|

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  8. Evaluate the following determinants: |(219,117,345),(19,9,34),(7,3,5...

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  9. Evaluate the following determinants : {:|(0,2,0),(2,3,4),(4,5,6)|

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  10. Evaluate the following determinant|(2,-1,0,1),(-3,0,1,-2),(1,1,-1,1),(...

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  11. Evaluate the determinant |(1^2, 2^2, 3^2,4^2),(2^2,3^2,4^2,5^2),(3^2,4...

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  12. Without expanding, prove that |(6,2,3),(9,3,5),(12,4,7) = 0

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  13. Use properties of determinants ot evaluate: {:|(x+y,y+z,z+x),(z,x,y)...

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  14. Evaluate the following determinants: |(0,c,b),(c,0,a),(-b,-a,0)|

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  15. By using determinants, find the area of the triangle whose vertices ar...

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  16. By using determinants, find the area of the triangle whose vertices ar...

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  17. Find the area of the triangle whose vertices are (-2, -3), (3, 2) and ...

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  18. By using determinants, find the area of the triangle whose vertices ar...

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  19. By using determinants, find the area of the triangle whose vertices ar...

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  20. Find the value of 'x' if the area of triangle is 35 square cm. With ve...

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