HSC Arts Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Choose the correct alternative:

`int "e"^(sqrt(x)) "d"x` is

Find the principal value of the following:

`sin^-1 (- 1/2)`

Find the principal value of the following:

tan^-1 (-1)

Find the principal value of the following:

cosec^-1 (2)

Find the principal value of the following:

`sec^-1 (-sqrt2)`

Prove that:

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

Prove that:

`tan^-1 (4/3) + tan^-1 (1/7) = pi/4`

Show that `tan^-1 (1/2) + tan^-1 (2/11) = tan^-1 (3/4)`

Solve `tan^-1 2x + tan^-1 3x = pi/4`

Solve: tan^-1 (x + 1) + tan^-1 (x – 1) = `tan^-1 (4/7)`

Evaluate:

`cos[tan^-1 (3/4)]`

Evaluate: sin`[1/2 cos^-1 (4/5)]`

Evaluate: `cos (sin^-1 (4/5) + sin^-1 (12/13))`

Prove that `tan^-1 (m/n) - tan^-1 ((m - n)/(m + n)) = pi/4`

Show that `sin^-1 (- 3/5) - sin^-1 (- 8/17) = cos^-1 (84/85)`

Express `tan^-1 [(cos x)/(1 - sin x)], - pi/2 < x < (3pi)/2` in the simplest form.

Express `tan^-1 ((cos x - sin x)/(cos x + sin x))`, 0 < x < π in the simplest form.

Simplify: `(125)^(2/3)`

Simplify: `16^((-3)/4)`

Simplify: `(- 1000)^((-2)/3)`