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Solve the following equations: sin^(-1)...

Solve the following equations: `sin^(-1)((3x)/5)+sin^(-1)((4x)/5)=sin^(-1)x` `sin^(-1)6x+sin^(-1)6sqrt(3)x=pi/2`

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. If cos^(-1)(x/a)+cos^(-1)(y/b)=alpha, prove that (x^2)/(a^2)-2(x y)/(...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. If tan^(-1)x+tan^(-1)y=pi/4, then write the value of x+y+x ydot

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  20. Prove that 2tan^(-1)(sqrt((a-b)/(a+b))tan(theta/2))=cos^(-1)((acosthet...

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