Advertisements
Advertisements
प्रश्न
Evaluate the following:
`cot^-1(cot (19pi)/6)`
Advertisements
उत्तर
We know that
cot-1 (cot θ) = θ, (0, π)
We have
`cot^-1(cot (19pi)/6)=cot^-1[cot(pi+pi/6)]`
`=cot^-1(cot pi/6)`
`=pi/6`
APPEARS IN
संबंधित प्रश्न
Solve for x:
`2tan^(-1)(cosx)=tan^(-1)(2"cosec" x)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`cos^-1{cos ((4pi)/3)}`
Evaluate the following:
`cos^-1(cos5)`
Evaluate the following:
`tan^-1(tan (9pi)/4)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Evaluate the following:
`cosec^-1{cosec (-(9pi)/4)}`
Write the following in the simplest form:
`tan^-1(x/(a+sqrt(a^2-x^2))),-a<x<a`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Evaluate the following:
`sin(tan^-1 24/7)`
Prove the following result
`sin(cos^-1 3/5+sin^-1 5/13)=63/65`
Solve: `cos(sin^-1x)=1/6`
Evaluate:
`cot{sec^-1(-13/5)}`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x > 0
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
If `(sin^-1x)^2+(cos^-1x)^2=(17pi^2)/36,` Find x
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
`sin^-1 63/65=sin^-1 5/13+cos^-1 3/5`
Evaluate the following:
`sin(1/2cos^-1 4/5)`
Evaluate the following:
`sin(2tan^-1 2/3)+cos(tan^-1sqrt3)`
`sin^-1 4/5+2tan^-1 1/3=pi/2`
If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.
Write the value of
\[\cos^{- 1} \left( \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\].
Evaluate sin
\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]
Write the value of cos−1 \[\left( \cos\frac{5\pi}{4} \right)\]
If 4 sin−1 x + cos−1 x = π, then what is the value of x?
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 principal value of \[\cos^{- 1} \left( \cos680^\circ \right)\]
Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the value of \[\sec^{- 1} \left( \frac{1}{2} \right)\]
The set of values of `\text(cosec)^-1(sqrt3/2)`
If \[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\] , find the value of x.
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
If \[\cos^{- 1} \frac{x}{a} + \cos^{- 1} \frac{y}{b} = \alpha, then\frac{x^2}{a^2} - \frac{2xy}{ab}\cos \alpha + \frac{y^2}{b^2} = \]
The number of real solutions of the equation \[\sqrt{1 + \cos 2x} = \sqrt{2} \sin^{- 1} (\sin x), - \pi \leq x \leq \pi\]
If \[\cos^{- 1} x > \sin^{- 1} x\], then
If y = sin (sin x), prove that \[\frac{d^2 y}{d x^2} + \tan x \frac{dy}{dx} + y \cos^2 x = 0 .\]
The equation sin-1 x – cos-1 x = cos-1 `(sqrt3/2)` has ____________.
