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Prove that:(9pi)/8-9/4sin^(-1)(1/3)=9/4s...

Prove that:`(9pi)/8-9/4sin^(-1)(1/3)=9/4sin^(-1)((2sqrt(2))/3)`

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L.H.S. `=\frac{9 \pi}{8}-\frac{9}{4} \sin ^{-1} \frac{1}{3}` $$ \begin{aligned} &=\frac{9}{4}\left(\frac{\pi}{2}-\sin ^{-1} \frac{1}{3}\right) \\ &=\frac{9}{4}\left(\cos ^{-1} \frac{1}{3}\right) \ldots .(1) \end{aligned} $$ ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Prove that: sin^(-1)((63)/(65))=sin^(-1)(5/(13))+cos^(-1)(3/5)

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  2. Prove that : tan^(-1)((63)/(16))=sin^(-1)(5/(13))+cos^(-1)(3/5)

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  3. Prove that:(9pi)/8-9/4sin^(-1)(1/3)=9/4sin^(-1)((2sqrt(2))/3)

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  4. solve:sin^-1x+sin^-1 2x=pi/3

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  5. Prove that: tan^(-1)4/5+cos^(-1)(12)/(13)=cos^(-1)(33)/(65)

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  6. Show that sin^(-1)(3/5)-sin^(-1)(8/(17))=cos^(-1)((84)/(85)) .

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

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  8. 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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  9. If cos^(-1) (x/2) + cos^(-1) (y/3) =alpha then prove that 9x^2-12xycos...

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  10. Solve the equation: cos^(-1)(a/x)-cos^(-1)(b/x)=cos^(-1)(1/a)

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  11. cos^(- 1)xsqrt(3)+cos^(- 1)x=pi/2

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  12. Prove that cos^(-1)(4/5)cos^(-1)((12)/(13))=cos^(-1)((33)/(65))

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  13. Evaluate: sin(2\ sin^(-1)0. 6)

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  14. Evaluate: sin(3\ sin^(-1)0. 4)

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  15. Prove the following: tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3...

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  16. Prove that: 2tan^(-1)(1/2)+tan^(-1)(1/7)=tan^(-1)((31)/(17))

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  17. Evaluate: tan(2tan^(-1)(1/5))

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  18. Prove that 2sin^-1[3/5]-tan^-1[17/31]=pi/4

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  19. Prove that : tan(1/2){sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))...

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  20. FInd the value of sin[2cot^(- 1)(- 5/12)]

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