Advertisements
Advertisements
Question
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
Advertisements
Solution
\[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right) = \cos^{- 1} \left[ \cos\left( 4\pi + \frac{2\pi}{3} \right) \right]\]
\[ = \cos^{- 1} \left( \cos\frac{2\pi}{3} \right)\]
\[ = \frac{2\pi}{3}\]
APPEARS IN
RELATED QUESTIONS
Prove that :
`2 tan^-1 (sqrt((a-b)/(a+b))tan(x/2))=cos^-1 ((a cos x+b)/(a+b cosx))`
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
Solve for x:
`2tan^(-1)(cosx)=tan^(-1)(2"cosec" x)`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy.
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
If `(sin^-1x)^2 + (sin^-1y)^2+(sin^-1z)^2=3/4pi^2,` find the value of x2 + y2 + z2
`sin^-1(sin (17pi)/8)`
`sin^-1(sin12)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`tan^-1(tan (9pi)/4)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`sin(sec^-1 17/8)`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`
Evaluate:
`cos(sec^-1x+\text(cosec)^-1x)`,|x|≥1
Solve the following equation for x:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
Evaluate the following:
`tan 1/2(cos^-1 sqrt5/3)`
If `sin^-1 (2a)/(1+a^2)-cos^-1 (1-b^2)/(1+b^2)=tan^-1 (2x)/(1-x^2)`, then prove that `x=(a-b)/(1+ab)`
Prove that
`sin{tan^-1 (1-x^2)/(2x)+cos^-1 (1-x^2)/(2x)}=1`
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:
`cos(sec^-1x+\text(cosec)^-1x),` | x | ≥ 1
Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
Write the difference between maximum and minimum values of sin−1 x for x ∈ [− 1, 1].
Write the value of sin (cot−1 x).
Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
If \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find x.
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
2 tan−1 {cosec (tan−1 x) − tan (cot−1 x)} is equal to
sin\[\left[ \cot^{- 1} \left\{ \tan\left( \cos^{- 1} x \right) \right\} \right]\] is equal to
\[\text{ If } u = \cot^{- 1} \sqrt{\tan \theta} - \tan^{- 1} \sqrt{\tan \theta}\text{ then }, \tan\left( \frac{\pi}{4} - \frac{u}{2} \right) =\]
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
If 2 tan−1 (cos θ) = tan−1 (2 cosec θ), (θ ≠ 0), then find the value of θ.
tanx is periodic with period ____________.
The equation sin-1 x – cos-1 x = cos-1 `(sqrt3/2)` has ____________.
