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

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

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`sin^(−1)x+sin^(−1)2x=π/3`
`θ=sin^(−1)x;ϕ=sin^(−1)2x.`
`θ+ϕ=π/3`
`ϕ=π/3−θ`
`sinϕ=sin(π/3−θ)`
`2x=sin(π/3)​cosθ−cos(π/3)​sinθ`
`2x=sqrt(3)/2 sqrt(​​1−x^2) ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. If cos^(-1)x+cos^(-1)y+cos^(-1)=pi, prove that x^2+y^2+z^2+2x y z=1.

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

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

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

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

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

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

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

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

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

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

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  12. Evaluate: sin(cot^(-1)x) (ii) cos(tan^(-1)x)

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

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

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  15. Prove that: sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15 and tan^2(s...

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

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

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  18. Find the value of the expression sin[cot^(-1){cos(tan^-1 1)}]

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

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

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