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Prove that, {cos(sin^(-1)x)}^2 = {sin(co...

Prove that, `{cos(sin^(-1)x)}^2 = {sin(cos^(-1)x)}^2 `.

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UNITED BOOK HOUSE-SET 13-EXERCISE
  1. CHOOSE the correct answer from the following alternative :P(A)=3/7,P(B...

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  2. If X follows a binomial distribution with parameter n = 101 and p = 1/...

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  3. Prove that, {cos(sin^(-1)x)}^2 = {sin(cos^(-1)x)}^2 .

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  4. Find the real values of K for which the following system of linear equ...

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  5. If A = [[cos alpha,sin alpha],[-sin alpha,cos alpha]] then prove that,...

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  6. Examine whether f(x) = |x| has a derivative at x = 0.

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  7. State Lagrange's mean value theorem.

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  8. Evaluate:int(sin x dx)/(cos 2x)

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  9. Find the integrating factor of the differential equation (x + y + 1)(d...

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  10. Prove that the function(sin(x + alpha))/(sin(x + beta)) has neither a ...

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  11. Using the method of differentail find the approximate value of sqrt 0....

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  12. A variable plane moves in such a way that the sum of the reciprocals o...

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  13. If A and B are two independent events, prove that A^C and B are also i...

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  14. Five cards are drawn successively with replacement from a well-shuffle...

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  15. If sin(alpha + beta) = 4/5 and sin (alpha - beta)= 5/13, find the valu...

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  16. If A and B are tow matrices such that AB =O, can we deduce that eithe...

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  17. (AB)^(-1) = B^(-1)A ^(-1) where A and B are invertible matrices satisf...

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  18. Answer the foll. Question : 2.show that |[1+a,1,1],[1,1+b,1],[1,1,1+c]...

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  19. Evaluate:int (dx)/(sqrt (sin^3 xsin(x+alpha)

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  20. Evaluate: int(log(logx)+1/((logx)^2))dx

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