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Show that [(1, - tantheta/2),(tantheta/2...

Show that `[(1, - tantheta/2),(tantheta/2, 1)][(1, tantheta/2),(-tantheta/2,1)]^-1 = [(costheta,- sin theta),(sintheta, cos theta)]`

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Solve the equation (1-tantheta)(1+sin2theta)=1+tantheta

sin^2theta+cos^2theta=1 .

Prove that (1+sin2theta)/(1-sin2theta)=((1+tantheta)/(1-tan theta))^(2)

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

Prove that (1+tan^2 theta)/(1+cot^2 theta)=((1-tantheta)/(1-cottheta))^2 .

If f(theta)=|{:(1,tantheta,1),(-tantheta,1,tantheta),(-1,-tantheta,1):}| then the set {f(theta):0lt=thetalt(pi)/(2)} is

Prove that : (1+costheta-sin^2 theta)/(sintheta(1+costheta))=cottheta .

Evaluate the determinants in exercises 1 to 2. |(cos theta, - sin theta),(sintheta, cos theta)]

If A = [(sintheta ,- costheta), (costheta, sintheta)] and B = [(costheta , sin theta),(-sintheta, cos theta)] . Compute (sin theta) A + (cos theta) B.

tantheta-cottheta=(2sin^2theta-1)/(sinthetacostheta)=(1-2cos^2theta)/(sinthetacostheta .

PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. If A= [(1,-1,1),(2,-1,0),(1,0,0)] and B = [(1,3,2),(1,1,1),(2,-3,-1)],...

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  2. Compute (AB)^-1 where A = [(1,3,3),(1,4,3),(1,3,4)] and B^-1 = [(2,1,...

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  3. Show that [(1, - tantheta/2),(tantheta/2, 1)][(1, tantheta/2),(-tanthe...

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  4. Find the inverse of the matrix A = {:[(a,b),(c,(1+bc)/a)] and show tha...

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  5. For the matrix A=[{:(3,2),(1,1):}], find the numbers a and b such that...

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  6. If A=[(2,-3),(-4,7)] compute A^(-1) and show that 2A^(-1) + A-9I =0

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  7. Find A^(-1) if A=[(0,1,1),(1,0,1),(1,1,0)] and show that A^(-1)=(A^2-3...

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  8. Show that A = [(-8,5),(2,4)] satsfies the equation x^2 + 4x - 42= 0. H...

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  9. If A = [(2,3,3),(3,2,3),(3,3,2)], then show that A^2 - 7A - 8I = O

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  10. Find the matrix X satisfying X [(5,3),(-1,-2)]=[(14,7),(7,7)]

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  11. Find the matrix X satisfying. [(3,2),(7,5)] X [(-1,1),(-2,1)] = [(2,...

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  12. Find the matrix X satisfying. [(2,1),(5,3)] X [(5,3),(3,2)] = [(1,0)...

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  13. Find the matrix X satisfying. [(2,1),(3,2) X [(-3,2),(5,-3)] = [(1,0...

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  14. If A = [(6,-7, 8),(1,-3,1),(2,1,-4)], compute det (adj A).

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  15. If A = [(3,2,2),(2,3,2),(2,2,3)], find adj (Adj A)

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  16. If A = [(1,0,2),(0,2,1),(2,0,3)], find A (adj A)

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  17. Prove that |(bc-a^2, ca-b^2, ab-c^2),(ca-b^2, ab-c^2, bc-a^2),(ab-c^2,...

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  18. Using matrix method solve the following systems of equations: (3x + ...

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  19. Using matrix method solve the following systems of equations: {:(3x ...

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  20. Using matrix method solve the following systems of equations: {:(2x ...

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