Advertisements
Advertisements
प्रश्न
Solve the following equation for x:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
Advertisements
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
Prove that :
`2 tan^-1 (sqrt((a-b)/(a+b))tan(x/2))=cos^-1 ((a cos x+b)/(a+b cosx))`
If (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
`sin^-1(sin (5pi)/6)`
`sin^-1(sin4)`
Evaluate the following:
`tan^-1(tan (9pi)/4)`
Evaluate the following:
`sec^-1(sec (13pi)/4)`
Evaluate the following:
`\text(cosec)^-1(\text{cosec} pi/4)`
Evaluate the following:
`cot^-1(cot pi/3)`
Write the following in the simplest form:
`cot^-1 a/sqrt(x^2-a^2),| x | > a`
Write the following in the simplest form:
`tan^-1{x+sqrt(1+x^2)},x in R `
Evaluate the following:
`sin(sin^-1 7/25)`
Evaluate the following:
`cosec(cos^-1 3/5)`
Evaluate the following:
`sec(sin^-1 12/13)`
`sin^-1x=pi/6+cos^-1x`
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
Solve the following equation for x:
`tan^-1 x/2+tan^-1 x/3=pi/4, 0<x<sqrt6`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
Solve the equation `cos^-1 a/x-cos^-1 b/x=cos^-1 1/b-cos^-1 1/a`
`4tan^-1 1/5-tan^-1 1/239=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 x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.
Write the range of tan−1 x.
Write the value of sin−1 (sin 1550°).
Evaluate sin
\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]
Write the value of cos2 \[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
Wnte the value of\[\cos\left( \frac{\tan^{- 1} x + \cot^{- 1} x}{3} \right), \text{ when } x = - \frac{1}{\sqrt{3}}\]
If \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} - \sqrt{1 - x^2}}{\sqrt{1 + x^2} + \sqrt{1 - x^2}} \right)\] = α, then x2 =
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 =
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
If x > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find \[\frac{dy}{dx}\] When \[\theta = \frac{\pi}{3}\] .
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.
Find the domain of `sec^(-1) x-tan^(-1)x`
Find the simplified form of `cos^-1 (3/5 cosx + 4/5 sin x)`, where x ∈ `[(-3pi)/4, pi/4]`
The value of sin `["cos"^-1 (7/25)]` is ____________.
The equation sin-1 x – cos-1 x = cos-1 `(sqrt3/2)` has ____________.
