Advertisements
Advertisements
प्रश्न
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
Advertisements
उत्तर
We know that
\[\cot^{- 1} \left( - x \right) = \pi - \cot^{- 1} \left( x \right)\] Therefore, the value of \[\cot^{- 1} \left( - x \right)\] for all `x in R` in terms of `cot^-1(x)` is `pi-cot^-1(x)`
APPEARS IN
संबंधित प्रश्न
Find the principal values of the following:
`cos^-1(-1/sqrt2)`
`sin^-1(sin pi/6)`
`sin^-1(sin (5pi)/6)`
`sin^-1(sin3)`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`tan^-1(tan pi/3)`
Evaluate the following:
`cot^-1(cot pi/3)`
Evaluate the following:
`sin(tan^-1 24/7)`
Evaluate the following:
`sin(sec^-1 17/8)`
Evaluate the following:
`tan(cos^-1 8/17)`
Prove the following result-
`tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5`
Evaluate:
`cos{sin^-1(-7/25)}`
Solve the following equation for x:
tan−1(x + 1) + tan−1(x − 1) = tan−1`8/31`
Sum the following series:
`tan^-1 1/3+tan^-1 2/9+tan^-1 4/33+...+tan^-1 (2^(n-1))/(1+2^(2n-1))`
`sin^-1 63/65=sin^-1 5/13+cos^-1 3/5`
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
If `cos^-1 x/2+cos^-1 y/3=alpha,` then prove that `9x^2-12xy cosa+4y^2=36sin^2a.`
`tan^-1 1/4+tan^-1 2/9=1/2cos^-1 3/2=1/2sin^-1(4/5)`
Solve the following equation for x:
`tan^-1 1/4+2tan^-1 1/5+tan^-1 1/6+tan^-1 1/x=pi/4`
Solve the following equation for x:
`2tan^-1(sinx)=tan^-1(2sinx),x!=pi/2`
Write the value of sin (cot−1 x).
Write the range of tan−1 x.
Write the value of sin−1
\[\left( \sin( -{600}°) \right)\].
Write the value of cos\[\left( 2 \sin^{- 1} \frac{1}{3} \right)\]
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
Write the value of cos−1 (cos 350°) − sin−1 (sin 350°)
Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the principal value of `sin^-1(-1/2)`
Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
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 =
The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is
If \[\cos^{- 1} \frac{x}{a} + \cos^{- 1} \frac{y}{b} = \alpha, then\frac{x^2}{a^2} - \frac{2xy}{ab}\cos \alpha + \frac{y^2}{b^2} = \]
\[\text{ If }\cos^{- 1} \frac{x}{3} + \cos^{- 1} \frac{y}{2} = \frac{\theta}{2}, \text{ then }4 x^2 - 12xy \cos\frac{\theta}{2} + 9 y^2 =\]
If tan−1 3 + tan−1 x = tan−1 8, then x =
The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] is
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
