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Compute the following: {:[(sin(theta+p...

Compute the following:
`{:[(sin(theta+phi), cos(theta+phi)),(sin(theta - phi),cos(theta-phi))] +[(sin(theta-phi), cos(theta-phi)),(sin(theta+phi), cos(theta+phi))]`

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Prove that : (sin (x+theta))/(sin (x+phi))= cos (theta-phi)+ cot (x+phi)sin(theta-phi) .

Prove the following identity : (sin theta)/(1+cos theta)+ (sin theta)/(1-cos theta)= 2/(sin theta) .

Prove the following identity : sin^4 theta+ cos^4 theta= 1-2 sin^2 theta cos^2 theta .

Prove the following identity : sin^6 theta+ cos^6 theta= 1-3 sin^2 theta cos^2 theta .

Prove the following : sin theta+ sin 3 theta+ sin 5 theta+sin 7 theta=4 cos theta cos2 theta sin4 theta .

Prove the following identity : (1-cos theta)/(sin theta)= (sin theta)/(1+cos theta) .

Prove the following identity : sin theta cot theta+ sin theta cosec theta=1 + cos theta .

Prove the following identity : (sin theta)/(1+cos theta)+ (tan theta)/(1+cos theta)= sec theta cosec theta- cot theta .

Prove the following identity : 2 (sin^6 theta+ cos^6 theta)-3 (sin^4 theta+ cos^4 theta)+1=0 .

MODERN PUBLICATION-MATRICES-EXERCISE
  1. Compute the following: : [[a,b],[-b,a]] + [[a,b],[b,a]]

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  2. Compute the following: : [[cos^2x,sin^2x],[sin^2x,cos^2x]] + [[sin^2x,...

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  3. Compute the following: {:[(sin(theta+phi), cos(theta+phi)),(sin(thet...

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  4. Compute the following: {:[(-2,3,-6),(8,5,16),(2,8,5)]+[(12,7,8),(8,0...

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  5. If A = {:[(2,-4),(4,2)], B = [(4,3),(-2,1)] and C = [(-2,-3),(-1,2)], ...

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  6. Does the sum {:[(5,3,2),(2,5,3),(5,2,3)] + [(0,0,0),(0,0,0)] make sens...

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  7. If A = {:[(1,-3,2),(2,0,2)], B = [(2,-1,-1),(1,0,-1)], find the matrix...

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  8. Given X = {:[(2,0,-2),(1,0,-2)] and Y = [(3,-1,0),(-2,0,-1)], find Z s...

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  9. Verify associative law of matrx addition for the matrices: A = {:[(1...

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  10. If A = {:[(1,2,3),(-1,0,2),(1,-3,-1)], B = [(4,5,6),(-1,0,1),(2,1,2)] ...

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  11. If A and B are two mxxn matrices and O is the null matrix of the type ...

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  12. Find the values of x,y,z and t, if: {:2[(x,z),(y,t)] + 3 [(1,-1),(0,...

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  13. If {:x[(2),(3)] + y [(-1,1)] = [(12),(6)], write the value. Of 'x'.

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  14. If {:2[(3,4),(5,x)] + [(1,y ),(0,1)] = [(7,0),(10,5)], find (x-y).

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  15. Find the vale of (x+y) from the following equation: {:2[(x,5),(7,y-3...

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  16. If A = {:[(4,2,7),(2,1,7)] and B = [(2,1,5),(3,4,6)] find 2A-B.

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  17. If A = {:[(8,0),(4,-2),(3,-6)] and B = [(2,-2),(4,2),(-5,1)], then fin...

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  18. If A = diag. [3,-5,7]^* and B - diag. [-1,2,4], then find (2A + 3B).

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  19. If A = [(2,7),(9,8)] and B = [(1,2),(0,3)], then find: (A-B).

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  20. If A = [(2,3),(-1,4)], find 2A

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