Advertisements
Advertisements
Question
Find the value of `tan^-1 (x/y)-tan^-1((x-y)/(x+y))`
Advertisements
Solution
We know
`tan^-1x-tan^-1y=tan^-1 (x-y)/(1+xy),xy>1`
Now,
`tan^-1 (x/y)-tan^-1((x-y)/(x+y))`
`=tan^-1{(x/y-(x-y)/(x+y))/(1+x/y((x-y)/(x+y)))}`
`=tan^-1{((x^2+xy-xy+y^2)/(y(x+y)))/((x^2+y^2+xy-xy)/(y(x+y)))}`
`=tan^-1 1`
`=tan^-1(tan pi/4)`
`=pi/4`
`thereforetan^-1(x/y)-tan^-1((x-y)/(x+y))=pi/4`
APPEARS IN
RELATED QUESTIONS
Find the value of the following: `tan(1/2)[sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))],|x| <1,y>0 and xy <1`
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
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.
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Evaluate the following:
`cosec^-1{cosec (-(9pi)/4)}`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Evaluate the following:
`sec(sin^-1 12/13)`
Evaluate the following:
`cos(tan^-1 24/7)`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
`tan^-1x+2cot^-1x=(2x)/3`
Solve the following equation for x:
tan−1(x + 1) + tan−1(x − 1) = tan−1`8/31`
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`
Prove that:
`2sin^-1 3/5=tan^-1 24/7`
`tan^-1 2/3=1/2tan^-1 12/5`
`2tan^-1 3/4-tan^-1 17/31=pi/4`
Show that `2tan^-1x+sin^-1 (2x)/(1+x^2)` is constant for x ≥ 1, find that constant.
Solve the following equation for x:
`tan^-1((2x)/(1-x^2))+cot^-1((1-x^2)/(2x))=(2pi)/3,x>0`
Solve the following equation for x:
`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`
Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
Write the value of sin (cot−1 x).
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 \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
The set of values of `\text(cosec)^-1(sqrt3/2)`
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 = \[\tan^{- 1} \left( \tan\frac{5\pi}{4} \right) \text{ and }\beta = \tan^{- 1} \left( - \tan\frac{2\pi}{3} \right)\] , then
The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is
If \[\sin^{- 1} \left( \frac{2a}{1 - a^2} \right) + \cos^{- 1} \left( \frac{1 - a^2}{1 + a^2} \right) = \tan^{- 1} \left( \frac{2x}{1 - x^2} \right),\text{ where }a, x \in \left( 0, 1 \right)\] , then, the value of x is
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
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 real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
