Advertisements
Advertisements
प्रश्न
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
Advertisements
उत्तर
\[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right) = \cos^{- 1} \left[ \cos\left( 4\pi + \frac{2\pi}{3} \right) \right]\]
\[ = \cos^{- 1} \left( \cos\frac{2\pi}{3} \right)\]
\[ = \frac{2\pi}{3}\]
APPEARS IN
संबंधित प्रश्न
Solve the following for x:
`sin^(-1)(1-x)-2sin^-1 x=pi/2`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
If `tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4` ,find the value of x
`sin^-1(sin4)`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Write the following in the simplest form:
`tan^-1{sqrt(1+x^2)-x},x in R`
Evaluate the following:
`cot(cos^-1 3/5)`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Solve: `cos(sin^-1x)=1/6`
Evaluate:
`cos(tan^-1 3/4)`
If `sin^-1x+sin^-1y=pi/3` and `cos^-1x-cos^-1y=pi/6`, find the values of x and y.
If `(sin^-1x)^2+(cos^-1x)^2=(17pi^2)/36,` Find x
`tan^-1x+2cot^-1x=(2x)/3`
Prove the following result:
`tan^-1 1/4+tan^-1 2/9=sin^-1 1/sqrt5`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
If `sin^-1 (2a)/(1+a^2)+sin^-1 (2b)/(1+b^2)=2tan^-1x,` Prove that `x=(a+b)/(1-ab).`
Find the value of the following:
`tan^-1{2cos(2sin^-1 1/2)}`
Find the value of the following:
`cos(sec^-1x+\text(cosec)^-1x),` | x | ≥ 1
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 < 0, then write the value of cos−1 `((1-x^2)/(1+x^2))` in terms of tan−1 x.
What is the value of cos−1 `(cos (2x)/3)+sin^-1(sin (2x)/3)?`
Write the value of cos−1 (cos 350°) − sin−1 (sin 350°)
Write the value of \[\sec^{- 1} \left( \frac{1}{2} \right)\]
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
Find the value of \[2 \sec^{- 1} 2 + \sin^{- 1} \left( \frac{1}{2} \right)\]
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
The positive integral solution of the equation
\[\tan^{- 1} x + \cos^{- 1} \frac{y}{\sqrt{1 + y^2}} = \sin^{- 1} \frac{3}{\sqrt{10}}\text{ is }\]
If \[\cos^{- 1} \frac{x}{2} + \cos^{- 1} \frac{y}{3} = \theta,\] then 9x2 − 12xy cos θ + 4y2 is equal to
If 4 cos−1 x + sin−1 x = π, then the value of x is
If tan−1 (cot θ) = 2 θ, then θ =
Prove that : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
Prove that : \[\cot^{- 1} \frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}} = \frac{x}{2}, 0 < x < \frac{\pi}{2}\] .
