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Prove the following statements "cot"^(...

Prove the following statements
`"cot"^(-1)9+"cosec"^(-1)sqrt(41)/(4)=pi/(4)`

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Directions Prove the following "tan"^(-1)1/(4)+"tan"^(-1)2/(9)=1/(2)"cos"^(-1)3/(5)=1/(2)"sin"^(-1)4/(5) .

SHARAM PUBLICATION-INVERSE TRIGNOMETRIC FUNCTIONS-EXAMPLE
  1. Using the principal values, find the value of cos^(-1)cos((13pi)/(6)).

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  2. Show that "sin"^(-1)(4)/(5) +2"tan"^(-1)(1)/(3) =(pi)/(2).

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  3. Prove the following statements "cot"^(-1)9+"cosec"^(-1)sqrt(41)/(4)=...

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  4. Find the value of tan(cos^(-1)(4/5)+tan^(-1)(2/3)).

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  5. Show that sin^(-1)(1/sqrt(10))+cos^(-1)(2/sqrt5)=pi/4.

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  6. Prove statement"tan"^2 "cos"^(-1)1/sqrt3 +"cot"^2 "sin"^-1 1/sqrt5 =6

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  7. Solve: sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x.

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  8. Prove that: sec^2(tan^(-1)3)-cosec^2(cot^(-1)3)=0

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  9. Evaluate "cos"(2"cos"^(-1)x+"sin"^(-1)x) at x=1/(5), where 0le"cos"^(-...

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  10. Prove that tan^(-1)sqrt(x) =(1)/(2) cos^(-1)((1-x)/(1+x)), x in (0, 1)...

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  11. Prove that: cos^(-1)(12/13)+sin^(-1)(3/5)=sin^(-1)(56/65)

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  12. Prove that: tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3)/(1-3x^2...

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  13. Directions (Q. Nos. 16-25) Prove the following "cos"["tan"^(-1){"sin...

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

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  15. Solve : tan^(-1)((1-x)/(1+x))=1/2tan^(-1)x

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  16. Solve for x, 2 tan ^(-1)(cos x) =tan^(-1) (2"cosec"x).

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  17. Solve: tan^(-1)x+2cot^(-1)x=(2pi)/3

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  18. Prove that cos^(-1)(x)+ cos^(-1){(x)/(2)+sqrt(3-3x^(2))/(2)}=(pi)/(3).

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  19. Prove that: cot^(-1)7+cot^(-1)18=cot^(-1)5.

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  20. Prove that: sin^(-1)(3/5)+sin^(-1)(8/17)=tan^(-1)(77/36).

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