PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

`sin^-1x=pi/6+cos^-1x`

`4sin^-1x=pi-cos^-1x`

`tan^-1x+2cot^-1x=(2x)/3`

`5tan^-1x+3cot^-1x=2x`

Prove the following result:

`tan^-1  1/7+tan^-1  1/13=tan^-1  2/9`

Prove the following result:

`sin^-1  12/13+cos^-1  4/5+tan^-1  63/16=pi`

Prove the following result:

`tan^-1  1/4+tan^-1  2/9=sin^-1  1/sqrt5`

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

Solve the following equation for x:

`tan^-1  2x+tan^-1  3x = npi+(3pi)/4`

Solve the following equation for x:

tan⁻¹(x + 1) + tan⁻¹(x − 1) = tan⁻¹`8/31`

Solve the following equation for x:

tan⁻¹(x −1) + tan⁻¹x tan⁻¹(x + 1) = tan⁻¹3x

Solve the following equation for x:

`tan^-1((1-x)/(1+x))-1/2 tan^-1x` = 0, where x > 0

Solve the following equation for x:

 cot⁻¹x − cot⁻¹(x + 2) =`pi/12`, x > 0

Solve the following equation for x:

tan⁻¹(x + 2) + tan⁻¹(x − 2) = tan⁻¹ `(8/79)`, x > 0

Solve the following equation for x:

`tan^-1  x/2+tan^-1  x/3=pi/4, 0<x<sqrt6`

Solve the following equation for x:

`tan^-1((x-2)/(x-4))+tan^-1((x+2)/(x+4))=pi/4`

Solve the following equation for x:

`tan^-1(2+x)+tan^-1(2-x)=tan^-1  2/3, where  x< -sqrt3 or, x>sqrt3`

Solve the following equation for x:

`tan^-1  (x-2)/(x-1)+tan^-1  (x+2)/(x+1)=pi/4`

Sum the following series:

`tan^-1  1/3+tan^-1  2/9+tan^-1  4/33+...+tan^-1  (2^(n-1))/(1+2^(2n-1))`

Evaluate: `cos(sin^-1  3/5+sin^-1  5/13)`