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If cos^(-1)(x/a)+cos^(-1)(y/b)=alpha, p...

If `cos^(-1)(x/a)+cos^(-1)(y/b)=alpha,` prove that `(x^2)/(a^2)-2(x y)/(a b)cosalpha+(y^2)/(b^2)=sin^2alpha`

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Solve the equation: cos^(-1)(a/x)-cos^(-1)(b/x)=cos^(-1)(1/b)-cos^(-1)...

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

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  3. If cos^(-1)(x/a)+cos^(-1)(y/b)=alpha, prove that (x^2)/(a^2)-2(x y)/(...

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  4. Solve sin^(-1)x+sin^(-1)2x=pi/3dot

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  5. Solve the following equations: sin^(-1)((3x)/5)+sin^(-1)((4x)/5)=sin^...

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  6. Prove that sin^(-1)(8/(17))+sin^(-1)(3/5)=cos^(-1)((36)/(85))

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  7. The value of tan^-1(1/3)+tan^-1(2/9)+tan^-1(4/33)+tan^-1(8/129)+....n ...

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  8. Find the value of tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))

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  9. Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(cota)+tan^(-1)(cot^3A)={0 when...

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  10. "If"sin{cot^(-1)(x+1)}=cos(tan^(-1)x), then find x.

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  11. Solve the following equation for x : "cos"(tan^(-1)x)=sin(cot^(-1)3/...

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  12. Write each of the following in the simplest form: cot^(-1){a/(sqrt(x...

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  13. Evaluate: sin(cot^(-1)x)

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  14. Simplify each of the following: sin^(-1)((sinx+cosx)/(sqrt(2)))

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  15. Evaluate the following: sin^(-1)(sin 10)

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  16. Prove that: sec(tan^-1 1)+cos e c(cot^(-1) 1)=4

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  17. Prove that: "sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^2+1)/(x^2+2))

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  18. Evaluate: sin(cos^(-1)3/5+cos e c^(-1)(13)/5)

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  19. Find the value of the expression sin[cot^(-1){cos (pi/2)}]

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  20. Write the value of sin{pi/3-sin^(-1)(-1/2)}

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