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Prove that tan (pi/4+1/2cos^(-1)""a/b)+t...

Prove that `tan (pi/4+1/2cos^(-1)""a/b)+tan(pi/4-1/2cos^(-1)""a /b)=(2b)/a`

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MODERN PUBLICATION-SAMPLE PAPER 2020-EXERCISE
  1. Prove that for any f:X rarr Y , f o idx = f =idY of.

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  2. Solve equation 3"tan"^(-1)1/((2+sqrt3)) - "tan"^(-1) 1/x ="tan"^(-1) 1...

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  3. Prove that tan (pi/4+1/2cos^(-1)""a/b)+tan(pi/4-1/2cos^(-1)""a /b)=(2b...

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  4. Two cards are drawn successively with replacement from a well-shuffled...

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  5. Find the inverse of the matrix [{:(4,-2),(3,1):}]

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  6. There are two families A and B. There are 4 men, 6 women and 2 childre...

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  7. Eliminate x,y,z from a=x/y-z, b=y/z-x, c=z/x-y

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  8. There are 25 girls and 15 boys in class XI and 30 boys and 20 girls in...

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  9. Show that the tangent to the curve x = a (t - sin t), y = at (1 + cos ...

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  10. If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

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  11. What is the derivative of sec^(-1)(1/(2x^2-1)),with respect to(sqrt(1...

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  12. Find the approximate value of sqrt(48.96)

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  13. Solve : In((dy)/(dx)) = 3x+4y given that y=0, when x=0.

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  14. int(2sinx+3cosx)/(3sinx+4cosx)dx=?

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  15. Evaluate the following integrals : int(0)^(pi//2)log|(4+3sinx)/(4+3c...

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  16. The area between x=y^(2) and x=4 is divided into two equal parts by th...

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  17. Solve : x(dy)/(dx) + y = y^2

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  18. Prove that the measure of the angle between two main diagonals of a cu...

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  19. Prove that the four points with position vectors 2veca+3vecb-vecc, vec...

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  20. If veca=3hati+hatj+2hatk,vecb=2hati-3hatj+4hatk then verify that vecat...

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