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Show that |(sin10^@, - cos10^@),(sin80^@...

Show that `|(sin10^@`, - cos10^@),(sin80^@, cos80^@)| = 1`

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Evaluate the following determinants: |(a+ib , - c + id),(c+id, a-ib)...

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  2. Evaluate the following determinants: |(3x, x-7),(x+1,5x+1)|

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  3. Show that |(sin10^@, - cos10^@),(sin80^@, cos80^@)| = 1

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  4. Show that {:|(cos15^@, sin15^@),(sin75^@, cos75^@)|:}= 0

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  5. Evaluate |(x,x+1),(x-1,x)|

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  6. Evaluate the following determinants: |(1,0,0),(0,1,0),(0,0,1)|

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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: |(1,0,2),(0,2,1),(2,0,3)|

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  9. Evaluate the following determinants: |(1,-3,1),(6,-7,8),(2,1,-4)|

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  10. Evaluate the following determinants: |(3,2,3),(2,2,3),(3,2,3)|

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  11. Evaluate the following determinants: |(a,h,g),(h,b,f),(g,f,c)|

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  12. If A = [(2,5),(3,1)] and B = [(4,-1),(1,3)], verify that det AB =(det ...

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  13. Evaluate :|(a,0,0,0),(0,b,0,0),(0,0,c,0),(0,0,0,d)|

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  14. Evaluate det A where A = [(2,0,0,1),(-3,0,1,0),(1,1,-1,1),(2,0,5,0)]

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  15. If |(3x,7),(-2,3)| = |(8,7),(-2,3)| find x.

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

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

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

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

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

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