Advertisements
Advertisements
प्रश्न
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
उत्तर
For `2cos^-1 2x` to be defined.
`-1<=2x<=1`
`=>-1/2<=x<=1/2` .....(i)
For `sin^-1x` to be defined.
`-1<=x<=1` .....(ii)
Domain of `f(x) = [-1/2,1/2]cap[-1,1]`
`=[-1/2,1/2]`.
APPEARS IN
संबंधित प्रश्न
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
`sin^-1(sin (7pi)/6)`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`cos^-1(cos3)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`tan^-1(tan pi/3)`
Evaluate the following:
`tan^-1(tan (9pi)/4)`
Evaluate the following:
`sec^-1(sec (5pi)/4)`
Evaluate the following:
`sec^-1(sec (7pi)/3)`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Prove the following result
`tan(cos^-1 4/5+tan^-1 2/3)=17/6`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x < 0
`4sin^-1x=pi-cos^-1x`
Find the value of `tan^-1 (x/y)-tan^-1((x-y)/(x+y))`
Solve the following equation for x:
tan−1(x −1) + tan−1x tan−1(x + 1) = tan−13x
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
If `sin^-1 (2a)/(1+a^2)-cos^-1 (1-b^2)/(1+b^2)=tan^-1 (2x)/(1-x^2)`, then prove that `x=(a-b)/(1+ab)`
If `sin^-1 (2a)/(1+a^2)+sin^-1 (2b)/(1+b^2)=2tan^-1x,` Prove that `x=(a+b)/(1-ab).`
Solve the following equation for x:
`tan^-1 1/4+2tan^-1 1/5+tan^-1 1/6+tan^-1 1/x=pi/4`
Solve the following equation for x:
`3sin^-1 (2x)/(1+x^2)-4cos^-1 (1-x^2)/(1+x^2)+2tan^-1 (2x)/(1-x^2)=pi/3`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
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 cos−1 (cos 350°) − sin−1 (sin 350°)
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
The set of values of `\text(cosec)^-1(sqrt3/2)`
Write the value of \[\tan^{- 1} \left( \frac{1}{x} \right)\] for x < 0 in terms of `cot^-1x`
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] is equal to
The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is
The value of \[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right)\] is
If 4 cos−1 x + sin−1 x = π, then the value of x is
In a ∆ ABC, if C is a right angle, then
\[\tan^{- 1} \left( \frac{a}{b + c} \right) + \tan^{- 1} \left( \frac{b}{c + a} \right) =\]
If x > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to
The value of tan `("cos"^-1 4/5 + "tan"^-1 2/3) =`
The equation sin-1 x – cos-1 x = cos-1 `(sqrt3/2)` has ____________.
