Advertisements
Advertisements
प्रश्न
Write the value of tan−1 x + tan−1 `(1/x)` for x < 0.
Advertisements
उत्तर
`tan^-1x+tan^-1y=tan^-1((x+y)/(1-xy))`
When `x<0,1/x<0,` then both are negative.
Let x = -y, y > 0
Then,
`tan^-1x+tan^-1 1/x=tan^-1 (-y)+tan^-1(-1/y)`
`=-(tan^-1y+tan^-1 1/y)`
`=-tan^-1((y+1/y)/(1-y1/y)), y>0`
`=-tan^-1((y^2+1)/0)`
`=-tan^-1(oo)`
`=-tan^-1(tan pi/2)`
`=pi/2`
`thereforetan^-1x+tan^-1 1/x=-pi/2, x<0`
APPEARS IN
संबंधित प्रश्न
Solve the equation for x:sin−1x+sin−1(1−x)=cos−1x
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
`sin^-1(sin pi/6)`
`sin^-1(sin (13pi)/7)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`cos^-1(cos4)`
Evaluate the following:
`cos^-1(cos5)`
Write the following in the simplest form:
`tan^-1{x+sqrt(1+x^2)},x in R `
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:
`cot(cos^-1 3/5)`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x > 0
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 − 2) = tan−1 `(8/79)`, x > 0
Evaluate the following:
`tan 1/2(cos^-1 sqrt5/3)`
Evaluate the following:
`sin(1/2cos^-1 4/5)`
`tan^-1 2/3=1/2tan^-1 12/5`
`sin^-1 4/5+2tan^-1 1/3=pi/2`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
Show that `2tan^-1x+sin^-1 (2x)/(1+x^2)` is constant for x ≥ 1, find that constant.
For any a, b, x, y > 0, prove that:
`2/3tan^-1((3ab^2-a^3)/(b^3-3a^2b))+2/3tan^-1((3xy^2-x^3)/(y^3-3x^2y))=tan^-1 (2alphabeta)/(alpha^2-beta^2)`
`where alpha =-ax+by, beta=bx+ay`
Write the value of cos\[\left( 2 \sin^{- 1} \frac{1}{3} \right)\]
Write the value of sin−1 (sin 1550°).
Evaluate sin
\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the principal value of \[\cos^{- 1} \left( \cos\frac{2\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{2\pi}{3} \right)\]
Write the value of \[\sec^{- 1} \left( \frac{1}{2} \right)\]
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
If \[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\] , find the value of x.
Find the value of \[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right)\]
The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is
The positive integral solution of the equation
\[\tan^{- 1} x + \cos^{- 1} \frac{y}{\sqrt{1 + y^2}} = \sin^{- 1} \frac{3}{\sqrt{10}}\text{ is }\]
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] is equal to
If tan−1 (cot θ) = 2 θ, then θ =
