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

Prove the following result-

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

If R is a relation on the set A = {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3)}, then R is ____________ .

Prove the following result

`sin(cos^-1  3/5+sin^-1  5/13)=63/65`

Solve: `cos(sin^-1x)=1/6`

 If A = {a, b, c, d}, then a relation R = {(a, b), (b, a), (a, a)} on A is _____________ .

If A = {1, 2, 3}, then a relation R = {(2, 3)} on A is _____________ .

Evaluate:

`cos{sin^-1(-7/25)}`

Let R be the relation on the set A = {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Then, _____________________ .

Evaluate:

`sec{cot^-1(-5/12)}`

Let A = {1, 2, 3}. Then, the number of equivalence relations containing (1, 2) is ______.

Evaluate:

`cot{sec^-1(-13/5)}`

The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is ___________________ .

Evaluate:

`tan{cos^-1(-7/25)}`

Evaluate:

`cosec{cot^-1(-12/5)}`

Evaluate:

`cos(tan^-1  3/4)`

Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`

Evaluate: 

`cot(sin^-1  3/4+sec^-1  4/3)`

Evaluate:

`sin(tan^-1x+tan^-1  1/x)` for x < 0

Evaluate:

`sin(tan^-1x+tan^-1  1/x)` for x > 0

Evaluate:

`cot(tan^-1a+cot^-1a)`