Advertisements
Advertisements
प्रश्न
Solve the following equation for x:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
उत्तर
⇒ `cot^-1(x)-cot^-1(x+2)=pi/12`
⇒ `tan^-1(1/x)+cot^-1(1/(x+2))=pi/12` `[because cot^-1x=tan^-1 1/x]`
⇒ `tan^-1((1/x-1/(x+2))/(1+1/(x(x+2))))=pi/12`
⇒ `tan^-1((2/(x(x+2)))/((x^2+2x+1)/(x(x+2))))=pi/12`
⇒ `tan^-1(2/(x^2+2x+1))=pi/12`
⇒ `(2/(x^2+2x+1))=tan pi/12`
⇒ `(2/(x^2+2x+1))=tan(pi/3-pi/4)`
⇒ `(2/(x^2+2x+1))=(tan pi/3-tan pi/4)/(1+tan pi/3xxtan pi/4`
⇒ `(2/(x^2+2x+1))=(sqrt3-1)/(sqrt3+1)`
⇒ `(2/(x^2+2x+1))=(sqrt3-1)/(sqrt3+1)xx(sqrt3+1)/(sqrt3+1)`
⇒ `(2/(x^2+2x+1))=2/(sqrt3+1)^2`
⇒ `1/(x+1)^2=1/(sqrt3+1)^2`
⇒ `x+1=sqrt3+1`
⇒ `x=sqrt3`
APPEARS IN
संबंधित प्रश्न
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
`sin^-1(sin pi/6)`
Evaluate the following:
`tan^-1(tan (7pi)/6)`
Write the following in the simplest form:
`tan^-1{sqrt(1+x^2)-x},x in R `
Evaluate the following:
`sin(sec^-1 17/8)`
Solve: `cos(sin^-1x)=1/6`
Evaluate:
`cos{sin^-1(-7/25)}`
Evaluate:
`cosec{cot^-1(-12/5)}`
`sin(sin^-1 1/5+cos^-1x)=1`
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
Evaluate the following:
`tan{2tan^-1 1/5-pi/4}`
Prove that:
`2sin^-1 3/5=tan^-1 24/7`
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=pi/2`
Solve the following equation for x:
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.
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 1540°).
Evaluate sin
\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]
Write the value of cos−1 (cos 350°) − sin−1 (sin 350°)
Write the value of sin−1 \[\left( \cos\frac{\pi}{9} \right)\]
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
Write the value of \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]
Show that \[\sin^{- 1} (2x\sqrt{1 - x^2}) = 2 \sin^{- 1} x\]
Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is
sin\[\left[ \cot^{- 1} \left\{ \tan\left( \cos^{- 1} x \right) \right\} \right]\] is equal to
If α = \[\tan^{- 1} \left( \frac{\sqrt{3}x}{2y - x} \right), \beta = \tan^{- 1} \left( \frac{2x - y}{\sqrt{3}y} \right),\]
then α − β =
If θ = sin−1 {sin (−600°)}, then one of the possible values of θ is
If \[3\sin^{- 1} \left( \frac{2x}{1 + x^2} \right) - 4 \cos^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) + 2 \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) = \frac{\pi}{3}\] is equal to
The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] is
If tan−1 (cot θ) = 2 θ, then θ =
If x > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to
The period of the function f(x) = tan3x is ____________.
Find the value of `sin^-1(cos((33π)/5))`.
