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If ABC is a triangle, then prove that a...

If ABC is a triangle, then prove that ` abs[[tanA,1,1],[1,tanB,1],[1,1,tanC]]=2`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Prove statement tan ( 2 "tan"^(-1)1/5-pi/4) + 7/17 =0

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  2. Prove that for any f:X rarr Y , f o idx = f =idY of.

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  3. If ABC is a triangle, then prove that abs[[tanA,1,1],[1,tanB,1],[1,1,...

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  4. Find B if B^(2)=[{:(17,8),(8,17):}]

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  5. If f(x)=[[1+sin^2x,cos^2x,4sin2x],[sin^2x,1+cos^2x,4sin2x],[sin^2x,cos...

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  6. Solve the following : [[x,1,3],[1,x,1],[3,6,3]]=0

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  7. If f(x) = a In x + bx^2 + x has extreme values at x= - 1 and x = 2 the...

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  8. If cos y = x cos(a+y) then prove that dy/dx = (cos^2(a+y))/sin a

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  9. If ysqrt(x^2 +1) = log{sqrt(x^2 +1)- x} then prove that (x^2 +1) dy/dx...

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  10. Find the equation of normal to the curve x^3 =4y which passes through ...

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  11. If y=x^2cos^(-1)(frac[sqrtx-1][sqrtx+1])+x^2cosec^(-1)(frac[sqrtx+1][...

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  12. Integrate int(frac[x-1][2x+1])dx

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  13. int0^2[x^2]dx

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  14. int0^(pi/2)e^x cosxdx

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  15. Solve(x log x )dy/dx+y=2 log x.

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  16. Find the area of the portion of the parabola y^2=4x bounded by the dou...

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  17. If the sum of two unit vectors is a unit vector, show that the magnitu...

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  18. Prove that : |veca + vecb|le|veca|+|vecb|.

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  19. If A (1,0,-1), B (-2,4,-2) and C(1,5,10) be the vertices of a triangle...

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  20. Find a symmetric form of the equation to the lines x +2y-z-2= 0 and 2x...

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