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Prove the following results: cot(cos^(-...

Prove the following results: `cot(cos^(-1)(4/5)+sin^(-1)(4/5))=0`

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Prove the following results: tan(sin^(-1)(5)/(13)+cos^(-1)3/5)=(63)/(16) (ii) sin(cos^(-1)3/5+sin^(-1)5/(13))=(63)/(65)

Prove the following: cos^(-1)((12)/(13))+sin^(-1)(3/5)=sin^(-1)((56)/(65))

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

Prove the following: tan^(-1)(1/4)+tan^(-1)(2/9)=1/2cos^(-1)(3/5)

Which of the following angles is greater? theta_1=sin^(-1)(4/5)+sin^(-1)(1/3)ortheta_2=cos^(-1)(4/5)+cos^(-1)(1/3)

Solve the following equation for x : "cos"(tan^(-1)x)=sin(cot^(-1)(3/4)) , tan(cos^(-1)x)=sin(cot^(-1)(1/2))

Prove The following: "cos"(sin^(-1)\ 3/5+cot^(-1)\ 3/2)=6/(5\ sqrt(13))

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Prove the following identities : cot^(2) A ((sec A - 1)/(1 + sin A)) + sec ^(2) A ((sin A -1)/ (1 + sec A)) = 0

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Solve: "cos"{cos^(-1)(x)}=0

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  2. Solve : "sin"(sin^(-1)x)=1/2

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  3. Prove the following results: cot(cos^(-1)(4/5)+sin^(-1)(4/5))=0

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  4. If a , b , c >0 and s=(a+b+c)/2, prove that tan^(-1)sqrt((2a s)/(b c...

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  5. If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+...

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  6. If ci >0 for i=1,2,....., n prove that tan^(-1)((c1x-y)/(c1y+x))+tan^...

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  7. Evaluate: tan^(-1)(1)+tan^(-1)(0),

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  8. Prove that: sum(m=1)^ntan^(-1)((2m)/(m^4+m^2+2))=tan^(-1)((n^2+n)/(n^2...

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  9. Sum the following series to infinity: tan^(-1)1/(1+1+1^2)+tan^(-1)1/(1...

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  10. Solve the equation: tan^-1(2x)+tan^-1 {(3x)} =pi/4

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  11. If a1,a2,a3, an are in arithmetic progression with common difference d...

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  12. Prove that: tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x...

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  13. If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)...

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  14. Find the maximum and minimum values of (sin^(-1)x)^3+(cos^(-1)x)^3, wh...

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  15. the greatest and least values of (sin^(-1) x)^2+(cos^(-1)x)^2

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  16. Solve : 4sin^(-1)x=pi-cos^(-1)x

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  17. If (sin^(-1)x)^2+(cos^(-1)x)^2=(17pi^2)/(36) , find xdot

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  18. Prove that : tan^(-1)2+tan^(-1)3=(3pi)/4

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  19. Prove that : tan^(-1)(2/11)+tan^(-1)(7/24)=tan^(-1)(1/2)

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  20. Prove that: sin^(-1)(12)/(13)+cos^(-1)4/5+tan^(-1)(63)/(16)=pi

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