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

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)`

`sin^-1  63/65=sin^-1  5/13+cos^-1  3/5`

`sin^-1  5/13+cos^-1  3/5=tan^-1  63/16`

`(9pi)/8-9/4sin^-1  1/3=9/4sin^-1  (2sqrt2)/3`

Solve the following:

`sin^-1x+sin^-1  2x=pi/3`

Solve the following:

`cos^-1x+sin^-1  x/2=π/6`

If `cos^-1  x/2+cos^-1  y/3=alpha,` then prove that  `9x^2-12xy cosa+4y^2=36sin^2a.`

Solve the equation `cos^-1  a/x-cos^-1  b/x=cos^-1  1/b-cos^-1  1/a`

Solve `cos^-1sqrt3x+cos^-1x=pi/2`

Prove that: `cos^-1  4/5+cos^-1  12/13=cos^-1  33/65`

Evaluate the following:

`tan{2tan^-1  1/5-pi/4}`

Evaluate the following:

`tan  1/2(cos^-1  sqrt5/3)`

Evaluate the following:

`sin(1/2cos^-1  4/5)`

Evaluate the following:

`sin(2tan^-1  2/3)+cos(tan^-1sqrt3)`

Prove that:

`2sin^-1  3/5=tan^-1  24/7`