Advertisements
Advertisements
प्रश्न
Find the domain of `f(x)=cos^-1x+cosx.`
उत्तर
For `cos^-1x` to be defined.
`-1<=x<=1`
Now, cosx is defined for all real values.
So, domain of cosx is R.
Domain of `f(x) is R cap[-1,1]=[-1,1]`.
APPEARS IN
संबंधित प्रश्न
Write the value of `tan(2tan^(-1)(1/5))`
Solve the equation for x:sin−1x+sin−1(1−x)=cos−1x
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
Find the principal values of the following:
`cos^-1(tan (3pi)/4)`
Evaluate the following:
`cos^-1(cos5)`
Evaluate the following:
`tan^-1(tan (7pi)/6)`
Evaluate the following:
`tan^-1(tan1)`
Evaluate the following:
`sec^-1(sec (7pi)/3)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`cosec^-1{cosec (-(9pi)/4)}`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Evaluate:
`cosec{cot^-1(-12/5)}`
Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
If `cot(cos^-1 3/5+sin^-1x)=0`, find the values of x.
Solve the following equation for x:
tan−1(x + 1) + tan−1(x − 1) = tan−1`8/31`
Solve the following equation for x:
`tan^-1 x/2+tan^-1 x/3=pi/4, 0<x<sqrt6`
Solve the following equation for x:
`tan^-1(2+x)+tan^-1(2-x)=tan^-1 2/3, where x< -sqrt3 or, x>sqrt3`
Solve the equation `cos^-1 a/x-cos^-1 b/x=cos^-1 1/b-cos^-1 1/a`
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=pi/2`
Show that `2tan^-1x+sin^-1 (2x)/(1+x^2)` is constant for x ≥ 1, find that constant.
If x < 0, then write the value of cos−1 `((1-x^2)/(1+x^2))` in terms of tan−1 x.
Write the value of sin (cot−1 x).
Write the value of sin−1
\[\left( \sin( -{600}°) \right)\].
Evaluate sin \[\left( \tan^{- 1} \frac{3}{4} \right)\]
Write the value of sin−1 \[\left( \cos\frac{\pi}{9} \right)\]
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the value of \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]
Show that \[\sin^{- 1} (2x\sqrt{1 - x^2}) = 2 \sin^{- 1} x\]
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the principal value of `sin^-1(-1/2)`
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
The positive integral solution of the equation
\[\tan^{- 1} x + \cos^{- 1} \frac{y}{\sqrt{1 + y^2}} = \sin^{- 1} \frac{3}{\sqrt{10}}\text{ is }\]
\[\text{ If } u = \cot^{- 1} \sqrt{\tan \theta} - \tan^{- 1} \sqrt{\tan \theta}\text{ then }, \tan\left( \frac{\pi}{4} - \frac{u}{2} \right) =\]
If tan−1 (cot θ) = 2 θ, then θ =
If y = sin (sin x), prove that \[\frac{d^2 y}{d x^2} + \tan x \frac{dy}{dx} + y \cos^2 x = 0 .\]
The equation sin-1 x – cos-1 x = cos-1 `(sqrt3/2)` has ____________.