Advertisements
Advertisements
Question
`tan^-1x+2cot^-1x=(2x)/3`
Advertisements
Solution
`tan^-1x+2cot^-1x=(2x)/3`
⇒ `tan^-1x+2(pi/2-tan^-1x)=(2pi)/3` `[becausecot^-1x=pi/2-tan^-1x]`
⇒ `tan^-1x+pi-2tan^-1x=(2pi)/3`
⇒ `tan^-1x=pi/3`
⇒ `x=tan pi/3=sqrt3`
APPEARS IN
RELATED QUESTIONS
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
Find the domain of `f(x)=cos^-1x+cosx.`
`sin^-1(sin3)`
`sin^-1(sin4)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`sec^-1(sec pi/3)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Evaluate the following:
`cosec^-1(cosec (3pi)/4)`
Evaluate the following:
`cosec^-1(cosec (13pi)/6)`
Write the following in the simplest form:
`sin^-1{(sqrt(1+x)+sqrt(1-x))/2},0<x<1`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Evaluate the following:
`cosec(cos^-1 3/5)`
Prove the following result
`tan(cos^-1 4/5+tan^-1 2/3)=17/6`
Evaluate:
`cosec{cot^-1(-12/5)}`
Evaluate:
`cot(tan^-1a+cot^-1a)`
`sin(sin^-1 1/5+cos^-1x)=1`
Solve the following equation for x:
`tan^-1((1-x)/(1+x))-1/2 tan^-1x` = 0, where x > 0
Solve the following equation for x:
`tan^-1((x-2)/(x-4))+tan^-1((x+2)/(x+4))=pi/4`
`sin^-1 63/65=sin^-1 5/13+cos^-1 3/5`
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
Evaluate the following:
`tan{2tan^-1 1/5-pi/4}`
Evaluate the following:
`tan 1/2(cos^-1 sqrt5/3)`
Evaluate the following:
`sin(2tan^-1 2/3)+cos(tan^-1sqrt3)`
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`
Show that \[\sin^{- 1} (2x\sqrt{1 - x^2}) = 2 \sin^{- 1} x\]
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the principal value of \[\sin^{- 1} \left\{ \cos\left( \sin^{- 1} \frac{1}{2} \right) \right\}\]
The positive integral solution of the equation
\[\tan^{- 1} x + \cos^{- 1} \frac{y}{\sqrt{1 + y^2}} = \sin^{- 1} \frac{3}{\sqrt{10}}\text{ is }\]
If sin−1 x − cos−1 x = `pi/6` , then x =
The number of solutions of the equation \[\tan^{- 1} 2x + \tan^{- 1} 3x = \frac{\pi}{4}\] is
If \[\cos^{- 1} x > \sin^{- 1} x\], then
Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
Find the simplified form of `cos^-1 (3/5 cosx + 4/5 sin x)`, where x ∈ `[(-3pi)/4, pi/4]`
