Advertisements
Advertisements
प्रश्न
Write the value of \[\tan^{- 1} \left( \frac{1}{x} \right)\] for x < 0 in terms of `cot^-1x`
Advertisements
उत्तर
\[\tan^{- 1} \left( \frac{1}{x} \right) = \tan^{- 1} \left( - \frac{1}{x} \right)\text{ for } x < 0\]
\[ = - \tan^{- 1} \left( \frac{1}{x} \right)\]
\[ = - \cot^{- 1} x\]
\[ = - \left( \pi - \cot^{- 1} x \right)\]
\[ = - \pi + \cot^{- 1} x\]
APPEARS IN
संबंधित प्रश्न
Solve the equation for x:sin−1x+sin−1(1−x)=cos−1x
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy.
Prove that
`tan^(-1) [(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))]=pi/4-1/2 cos^(-1)x,-1/sqrt2<=x<=1`
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
`sin^-1{(sin - (17pi)/8)}`
Evaluate the following:
`sec^-1(sec (7pi)/3)`
Evaluate the following:
`cosec^-1{cosec (-(9pi)/4)}`
Evaluate the following:
`cot^-1(cot (9pi)/4)`
Evaluate the following:
`cot^-1{cot (-(8pi)/3)}`
Evaluate the following:
`cosec(cos^-1 3/5)`
Prove the following result-
`tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5`
Solve the following equation for x:
`tan^-1 2x+tan^-1 3x = npi+(3pi)/4`
Solve the following equation for x:
tan−1(x −1) + tan−1x tan−1(x + 1) = tan−13x
`sin^-1 63/65=sin^-1 5/13+cos^-1 3/5`
Evaluate the following:
`sin(2tan^-1 2/3)+cos(tan^-1sqrt3)`
`tan^-1 2/3=1/2tan^-1 12/5`
Solve the following equation for x:
`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
Write the value of cos−1 \[\left( \cos\frac{5\pi}{4} \right)\]
If 4 sin−1 x + cos−1 x = π, then what is the value of x?
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the principal value of \[\cos^{- 1} \left( \cos\frac{2\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{2\pi}{3} \right)\]
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
If α = \[\tan^{- 1} \left( \tan\frac{5\pi}{4} \right) \text{ and }\beta = \tan^{- 1} \left( - \tan\frac{2\pi}{3} \right)\] , then
If x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals
If 4 cos−1 x + sin−1 x = π, then the value of x is
If x > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
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 ____________.
