Advertisements
Advertisements
प्रश्न
Find the domain of `sec^(-1)(3x-1)`.
Advertisements
उत्तर
The range of sec x is the domain of sec−1 x
Now,
The range of sec x is (−∞, −1] ∪ [1, ∞)
∴ The domain of a given function would be
3x − 1 ≤ −1 and 3x − 1 ≥ 1
3x ≤ 0 and 3x ≥ 2
x ≤ 0 and x ≥ `2/3`
∴ The domain of the given function is (−∞, 0] ∪ [`2/3`, ∞)
APPEARS IN
संबंधित प्रश्न
Find the value of the following: `tan(1/2)[sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))],|x| <1,y>0 and xy <1`
Prove that :
`2 tan^-1 (sqrt((a-b)/(a+b))tan(x/2))=cos^-1 ((a cos x+b)/(a+b cosx))`
`sin^-1(sin pi/6)`
`sin^-1(sin (7pi)/6)`
Evaluate the following:
`cos^-1{cos ((4pi)/3)}`
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`tan^-1(tan2)`
Evaluate the following:
`cosec^-1(cosec (3pi)/4)`
Evaluate the following:
`cot^-1{cot (-(8pi)/3)}`
Write the following in the simplest form:
`tan^-1sqrt((a-x)/(a+x)),-a<x<a`
Evaluate the following:
`sin(cos^-1 5/13)`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Evaluate:
`sec{cot^-1(-5/12)}`
Evaluate:
`cosec{cot^-1(-12/5)}`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x < 0
`tan^-1x+2cot^-1x=(2x)/3`
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 − 2) = tan−1 `(8/79)`, x > 0
Sum the following series:
`tan^-1 1/3+tan^-1 2/9+tan^-1 4/33+...+tan^-1 (2^(n-1))/(1+2^(2n-1))`
`tan^-1 1/7+2tan^-1 1/3=pi/4`
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)`
Prove that
`sin{tan^-1 (1-x^2)/(2x)+cos^-1 (1-x^2)/(2x)}=1`
If `sin^-1 (2a)/(1+a^2)+sin^-1 (2b)/(1+b^2)=2tan^-1x,` Prove that `x=(a+b)/(1-ab).`
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.
Evaluate sin
\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]
Write the value of sin−1 \[\left( \cos\frac{\pi}{9} \right)\]
Write the value of cos−1 \[\left( \cos\frac{5\pi}{4} \right)\]
If \[\sin^{- 1} \left( \frac{1}{3} \right) + \cos^{- 1} x = \frac{\pi}{2},\] then find x.
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`
Write the value of \[\sec^{- 1} \left( \frac{1}{2} \right)\]
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
Find the value of \[2 \sec^{- 1} 2 + \sin^{- 1} \left( \frac{1}{2} \right)\]
The value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
If \[\tan^{- 1} \left( \frac{1}{1 + 1 . 2} \right) + \tan^{- 1} \left( \frac{1}{1 + 2 . 3} \right) + . . . + \tan^{- 1} \left( \frac{1}{1 + n . \left( n + 1 \right)} \right) = \tan^{- 1} \theta\] , then find the value of θ.
