Arts (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

Find the range of the following function.

f(x) = x, x is a real number

Find the domain and the range of the real function f defined by `f(x)=sqrt((x-1))`

Let `f = {(x, x^2/(1+x^2)):x ∈ R}` be a function from R into R. Determine the range of f.

Prove that: `sin^2  pi/6 + cos^2  pi/3 - tan^2  pi/4 = -1/2`

Prove that  `2 sin^2  pi/6 + cosec^2  (7pi)/6 cos^2  pi/3 = 3/2`

Prove that  `cot^2  pi/6 + cosec  (5pi)/6 + 3 tan^2  pi/6 = 6`

Prove that: `2 sin^2  (3pi)/4 + 2 cos^2  pi/4  + 2 sec^2  pi/3 = 10`

Find the value of: sin 75°

Find the value of: tan 15°

Prove the following: `cos (pi/4 xx x) cos (pi/4 - y) - sin (pi/4 -  x)sin (pi/4  - y) =  sin (x + y)`

Prove the following: `(tan(pi/4 + x))/(tan(pi/4 - x)) = ((1+ tan x)/(1- tan x))^2`

Prove the following:

`(cos (pi + x) cos (-x))/(sin(pi - x) cos (pi/2 + x)) =  cot^2 x`

Prove the following:

`cos ((3pi)/ 2 + x ) cos(2pi + x) [cot ((3pi)/2 - x) + cot (2pi + x)]= 1`

Prove the following:

`cos ((3pi)/4 + x) - cos((3pi)/4 - x) = -sqrt2 sin x`

Prove the following:

cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)