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If A+B+C = pi, prove that [[sin^2A,cot...

If A+B+C = `pi`, prove that
`[[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,cotC,1]]`=0

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ARIHANT PRAKASHAN-VERY SIMILAR TEST 7-Section B (60 MARKS)
  1. IF A=[(1,tanx),(-tanx,1):}] then show that A^TA^-1=[(cos2x,-sin2x),(s...

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  2. Show that the following systems of linear equations is consistent and ...

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  3. If A+B+C = pi, prove that [[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,c...

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  4. Find the probability distribution of number of doublets in four throws...

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  5. Find the equasion of the tangents drawn from the point (1,2) to the cu...

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  6. Find the intervals in which the function y="sin"x,x in[0, 2pi] is in...

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  7. If y =(sin^(-1) x)^2, prove that (1-x^2)y2 - xy1 - 2 = 0

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  8. Differentiate "log"(10)x+"log"(x)10+"log"(x)x+"log"(10)10.

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  9. Verify the LMVT for the function f(x)=(1)/(4x-1),1lexle4.

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  10. Find the solution of the differential equation. (x-y-2)dx+(x-2y-3)dy...

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  11. Find the differential equation by eleminating the orbitary constants i...

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  12. Evaluate the following integrals : int(e^(6logx)-e^(5logx))/(e^(4log...

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  13. Prove that int(-1)^(1)log((2-x)/(2+x))dx=0

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  14. Find the area enclosed bt the two paraboles y^2=4 ax and x^2=4ay.

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  15. By computing shortest distance, determine whether the following pair o...

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  16. Find the equation of the plane Paralel to the plane 2x-y+3z+1=0 and at...

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  17. If vec(a), vec(b) and vec(c) are three mutually perpendicular vectors...

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  18. If vec(a),vec(b)" and "vec(c) are three vectors, such that vec(a)+vec(...

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  19. If hat(a), hat(b), hat(c) are unit vectors and hat(a) xx (hat(b) xx ha...

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  20. Evaluate "tan"("sin"^(-1)3/(5)+"cot"^(-1)3/(2)).

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