What is determinant value in composition matrix?(sin^2a cos^2a sinacosa) (sin^2b cos^2b sinbcosb) (sin^2c cos^2c sinccosc)

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should evaluate the determinant of the matrix using the properties of determinants.

Adding the second column to the first yields:

`((sin^2 a + cos^2 a, cos^2 a , sin a* cos a),(sin^2b + cos^2b, cos^2b , sin b* cos b),(sin^2c +cos^2c, cos^2c , sin c* cos c))`

You need to use the basic trigonometric formula:

`cos^2 alpha+ sin^2 alpha = 1`

Write the new form of the matrix:

`((1, cos^2 a , sin a* cos a),(1, cos^2b , sin b* cos b),(1, cos^2c , sin c* cos c))`

Calculating the determinant of the matrix yields:

`Delta = sin a*cos a(cos^2c - cos^2b) +sin b*cos b(cos^2a - cos^2c) + sin c*cos c(cos^2b - cos^2a)` 

The value of determinant of the matrix is `Delta = sin a*cos a(cos^2c - cos^2b) +sin b*cos b(cos^2a - cos^2c) + sin c*cos c(cos^2b - cos^2a).`

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