HSC Arts कक्षा ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions

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)`

Simplify: `(3^-6)^(1/3)`

Simplify: `(27^((-2)/3))/(27^((-1)/3))`

Evaluate `[((256)^(-1/2))^((-1)/4)]^3`

If `(x^(1/2) + x^(- 1/2))^2 = 9/2` then find the value of `(x^(1/2) - x^(-1/2))` for x >1

Simplify and hence find the value of n:

`(3^(2"n")*9^2*3^(-"n"))/(3^(3"n"))` = 27

Find the radius of the spherical tank whose volume is `(32pi)/3` units

. Simplify by rationalising the denominator `(7 + sqrt(6))/(3 - sqrt(2))`