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If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi, sho...

If `sin^(-1)x+sin^(-1)y+sin^(-1)z=pi`, show that `x^4+y^4+z^4+4x^2y^2z^2=2(x^2y^2+y^2z^2+z^2x^2)`

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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. If x=cos e c[tan^(-1){"cos"(cot^(-1)(sec(sin^(-1)a)))}] and y="sec"[...

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  2. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi , prove that: xsqrt(1-x^2)+ysqrt(1...

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  3. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi, show that x^4+y^4+z^4+4x^2y^2z^2=...

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  4. If tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha...

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  5. Prove that: tan{pi/4+1/2\ cos^(-1)(a/b)}+tan{pi/4-1/2\ cos^(-1)(a/b)}=...

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  6. Evaluate each of the following: sin(sin^(-1)(7/(25))) (ii) sin(cos^(...

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  7. Evaluate each of the following: sin(sec^(-1)(17)/8) (ii) "c o s e c...

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  8. Evaluate each of the following: (i)tan(cos^(-1)(8/(17))) (ii) cot(...

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  9. Prove the following results: tan(cos^(-1)4/5+tan^(-1)2/3)=(17)/6 (...

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  10. Prove the following results: tan(sin^(-1)(15)/(13)+cos^(-1)3/5)=(63...

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  11. Solve: cos(sin^(-1)x)=1/6

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  12. Solve: cos{2\ sin^(-1)(-x)}=0

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  13. Evaluate: cos{sin^(-1)(-5/(13))} (ii) cot{sin^(-1)(-7/(25))}

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  14. Evaluate: sec{sin^(-1)(-8/(17))}

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  15. Evaluate: sin{cos^(-1)(-3/5)} (ii) tan{cos^(-1)(-(12)/(13))}

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  16. Evaluate: "c o s e c"{cos^(-1)(-(12)/(13))}

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  17. Evaluate: sin{tan^(-1)(-7/(24))} (ii) cos{cot^(-1)(-5/(12))}

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  18. Evaluate: "c o s e c"{cot^(-1)(-4/3)}

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  19. Prove that: sin^(-1)(-4/5)=tan^(-1)(-4/3)=co^(-1)(-3/5)-pi

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  20. Prove that: tan^(-1)x+tan^(-1)1/x={pi/2,ifx >0-pi/2,ifx<0

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