Advertisements
Advertisements
Question
Prove that:
`2sin^-1 3/5=tan^-1 24/7`
Solution
= `2sin^-1 3/5 = 2tan^-1 3/sqrt(5^2 - 3^2)` ...`[sin^-1 "p"/"h" = tan^-1 "p"/sqrt("h"^2 - "p"^2)]`
= `2tan^-1 3/4`
= `tan^-1 (2 xx 3/4)/(1 - (3/4)^2)` ...`[2tan^-1 = tan^-1 (2x)/(1 - x^2)]`
= `tan^-1 (3/2)/(7/16)`
`= tan^-1 24/7`
APPEARS IN
RELATED QUESTIONS
If `cos^-1( x/a) +cos^-1 (y/b)=alpha` , prove that `x^2/a^2-2(xy)/(ab) cos alpha +y^2/b^2=sin^2alpha`
If (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
If `(sin^-1x)^2 + (sin^-1y)^2+(sin^-1z)^2=3/4pi^2,` find the value of x2 + y2 + z2
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
Find the domain of `f(x)=cos^-1x+cosx.`
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
`sin^-1(sin12)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`sec^-1(sec (7pi)/3)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`cosec^-1{cosec (-(9pi)/4)}`
Write the following in the simplest form:
`tan^-1{sqrt(1+x^2)-x},x in R `
Evaluate the following:
`sin(sin^-1 7/25)`
Evaluate the following:
`cosec(cos^-1 3/5)`
Evaluate the following:
`tan(cos^-1 8/17)`
Prove the following result
`tan(cos^-1 4/5+tan^-1 2/3)=17/6`
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
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−1(x − 1) = tan−1`8/31`
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`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
If `sin^-1 (2a)/(1+a^2)+sin^-1 (2b)/(1+b^2)=2tan^-1x,` Prove that `x=(a+b)/(1-ab).`
Solve the following equation for x:
`3sin^-1 (2x)/(1+x^2)-4cos^-1 (1-x^2)/(1+x^2)+2tan^-1 (2x)/(1-x^2)=pi/3`
If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.
Write the value of cos\[\left( 2 \sin^{- 1} \frac{1}{3} \right)\]
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the value of cos−1 \[\left( \cos\frac{5\pi}{4} \right)\]
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Find the value of \[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right)\]
If sin−1 x − cos−1 x = `pi/6` , then x =
The value of \[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right)\] is
If 4 cos−1 x + sin−1 x = π, then the value of x is
If tan−1 (cot θ) = 2 θ, then θ =
If y = sin (sin x), prove that \[\frac{d^2 y}{d x^2} + \tan x \frac{dy}{dx} + y \cos^2 x = 0 .\]
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.
