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Prove that 1/2cos^-1x=sin^-1sqrt((1-x)/2...

Prove that `1/2cos^-1x=sin^-1sqrt((1-x)/2)=cos^-1sqrt((1+x)/2)`.

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USHA PUBLICATION-RELATION AND FUNCTION INVERSE TRIGONOMETRIC FUNCTIONS LINEAR PROGRAMMING-EXERCISE
  1. Directions (Q. Nos. 16-25) Prove the following "cos"(2"tan"^(-1)1/(7...

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  2. Prove that 2tan^-1(cosectan^-1x-tancot^-1x=tan^-1x.

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  3. Prove that 1/2cos^-1x=sin^-1sqrt((1-x)/2)=cos^-1sqrt((1+x)/2).

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  4. If cos^-1x+cos^-1y+cos^-1z=pi, prove that x^2+y^2+z^2+2xyz=1.

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  5. Slove: tan(cos^-1x)=sin(cot^-1""1/2)

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  6. Find the feasible region of the inequations x+2ylt8, 2x+ylt8 and xgt0,...

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  7. Find the feasible region of the inequations 2x1+4x2gt40, 3x1+2x2gt60, ...

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  8. Shade the feasible region satisfying ineuations x1+2x2ge10, 2x1+2x2ge1...

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  9. Shade the feasible region satisfying ineuations x+2yle10, x+yge1, x-yl...

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  10. Shade the feasible region satisfying ineuations 4x+3yle60, 2x-yle0, x-...

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  11. Prove that the following sets A,B,C D are equivalent. WhereA={1,2,3,4,...

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  12. Let n be a positive integer,and a function f be defined as follows:{(0...

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  13. Let f be an invertible function . Then prove that (f^(-1))^(-1) = f.

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  14. If P(A/B) gt P(A) then prove that P(B/A) gt P(B)

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  15. If :f(x)=log((1+x)/(1-x)),then show that f(a)+f(b)=f((a+b)/(1+ab))and ...

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  16. If "sin"^(-1)(x/a) + "sin"^(-1) (y/b)=alpha "prove that" x^2/a^2+(2xy)...

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  17. If "sin"^(-1)(x/a) + "sin"^(-1) (y/b)=alpha "prove that" x^2/a^2+(2xy)...

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  18. Solve:Sin^-1x+sin^-1(1-x)=cos^1x

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  19. Solve sin^(-1)x +sin^(-1)(1-x) =(pi)/(2).

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  20. If: tan (pi cos""theta/2)=cot(pisin"theta/2),then show thattheta=sin^1...

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