Advertisements
Advertisements
प्रश्न
If x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals
पर्याय
`pi/2`
`-pi/2`
− π
none of these
Advertisements
उत्तर
(b) `-pi/2`
We know that
\[\tan^{- 1} x + \tan^{- 1} y = \tan^{- 1} \left( \frac{x + y}{1 - xy} \right)\]
\[x < 0, y < 0\] such that
xy = 1
Let x = -a and y = -b, where a and b both are positive.
\[\therefore \tan^{- 1} x + \tan^{- 1} y = \tan^{- 1} \left( \frac{x + y}{1 - xy} \right)\]
\[ = \tan^{- 1} \left( \frac{- a - a}{1 - 1} \right)\]
\[ = \tan^{- 1} \left( - \infty \right)\]
\[ = \tan^{- 1} \left\{ \tan\left( - \frac{\pi}{2} \right) \right\}\]
\[ = - \frac{\pi}{2}\]
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 (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
Prove that
`tan^(-1) [(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))]=pi/4-1/2 cos^(-1)x,-1/sqrt2<=x<=1`
If `tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4` ,find the value of x
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
Evaluate the following:
`cos^-1(cos3)`
Evaluate the following:
`sec^-1(sec pi/3)`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`sec^-1(sec (5pi)/4)`
Evaluate the following:
`\text(cosec)^-1(\text{cosec} pi/4)`
Evaluate the following:
`cosec^-1(cosec (11pi)/6)`
Evaluate the following:
`cosec^-1(cosec (13pi)/6)`
Evaluate the following:
`cosec^-1{cosec (-(9pi)/4)}`
Evaluate the following:
`cot^-1(cot (9pi)/4)`
Evaluate the following:
`cot^-1(cot (19pi)/6)`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Evaluate the following:
`cosec(cos^-1 3/5)`
Prove the following result
`sin(cos^-1 3/5+sin^-1 5/13)=63/65`
If `cot(cos^-1 3/5+sin^-1x)=0`, find the values of x.
`sin(sin^-1 1/5+cos^-1x)=1`
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`
`(9pi)/8-9/4sin^-1 1/3=9/4sin^-1 (2sqrt2)/3`
Evaluate the following:
`tan{2tan^-1 1/5-pi/4}`
`tan^-1 1/7+2tan^-1 1/3=pi/4`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
If −1 < x < 0, then write the value of `sin^-1((2x)/(1+x^2))+cos^-1((1-x^2)/(1+x^2))`
If tan−1 x + tan−1 y = `pi/4`, then write the value of x + y + xy.
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
Write the principal value of \[\sin^{- 1} \left\{ \cos\left( \sin^{- 1} \frac{1}{2} \right) \right\}\]
The set of values of `\text(cosec)^-1(sqrt3/2)`
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
sin \[\left\{ 2 \cos^{- 1} \left( \frac{- 3}{5} \right) \right\}\] is equal to
The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] 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
Prove that : \[\cot^{- 1} \frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}} = \frac{x}{2}, 0 < x < \frac{\pi}{2}\] .
