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Prove the following results: tan(cos^(...

Prove the following results: `tan(cos^(-1)(4/5)+tan^(-1)(2/3))=(17)/6`

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`tan(cos^(-1)(4/5)+tan^(-1)(2/3))`
=`tan(tan^(-1)((sqrt(5^2-4^2)/4)+tan^(-1)(2/3))`
=`tan(tan^(-1)((sqrt(3)/4)+tan^(-1)(2/3))`
=`tan(tan^(-1)((3/4+2/3)/(1-3/4xx2/3)))`
=`tan(tan^(-1)(17/6))`
...
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cos^(-1)(15/17)+2 tan^(-1)(1/5)=

Which of the following is/are correct? tan[cos^(-1)(4)/(5)+tan^(-1)(2)/(3)]=(17)/(6)cos[tan^(-1)(1)/(3)+tan^(-1)(1)/(2)]=(1)/(sqrt(2))cos2tan^(-1)((1)/(3))+cos(tan^(-1)2sqrt(2))=(14)/(15)cos[2cos^(-1)(1)/(5)+sin^(-1)(1)/(5)]=-(2sqrt(6))/(6)

tan(cos^(-1)((3)/(5))+tan^(-1)((1)/(4)))

Prove the following results: tan((sin^(-1)(15))/(13)+(cos^(-1)3)/(5))=(63)/(16) (ii) sin((cos^(-1)3)/(5)+(sin^(-1)5)/(13))=(63)/(65)

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

Prove the following: 2\ tan^(-1)3/4-tan^(-1)(17)/(31)=tan^(-1)pi/4

prove tan^(-1)(3/5)+tan^(-1)(1/4)=(pi)/(4)

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

Prove the following: 4tan^(-1)(1)/(5)-tan^(-1)(1)/(70)+tan^(-1)(1)/(99)=(pi)/(4)2tan^(-1)(1)/(5)+sec^(-1)(5sqrt(2))/(7)+2tan^(-1)(1)/(8)=(pi)/(4)

Prove that cos^(-1)((4)/(5))=tan^(-1)((3)/(4))

RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Solve: "cos"{2sin^(-1)(-x)}=0

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  2. Solve : "cos"(sin^(-1)x)=1/6

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  3. Prove the following results: tan(cos^(-1)(4/5)+tan^(-1)(2/3))=(17)/6

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  4. If a , b , c >0 and s=(a+b+c)/2,p rov et h a t tan^(-1)sqrt((2a s)/(b...

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

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  7. Evaluate: tan^(-1)((3sin2alpha)/(5+3cos2alpha))+tan^(-1)(1/4 tan alpha...

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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/(...

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  10. Solve the equation: tan^(-1)sqrt(x^2+x)+sin^(-1)sqrt(x^2+x+1)=pi/2

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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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