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

`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`

`tan^-1  1/4+tan^-1  2/9=1/2cos^-1  3/2=1/2sin^-1(4/5)`

`tan^-1  2/3=1/2tan^-1  12/5`

`tan^-1  1/7+2tan^-1  1/3=pi/4`

`sin^-1  4/5+2tan^-1  1/3=pi/2`

`2sin^-1  3/5-tan^-1  17/31=pi/4`

`2tan^-1  1/5+tan^-1  1/8=tan^-1  4/7`