Advertisements
Advertisements
प्रश्न
The value of \[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right)\] is
विकल्प
`pi/2`
`(5pi)/3`
`(10pi)/3`
0
उत्तर
(d) 0
We have
\[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right) = \cos^{- 1} \left\{ \cos\left( 2\pi - \frac{\pi}{3} \right) \right\} + \sin^{- 1} \left\{ \sin\left( 2\pi - \frac{\pi}{3} \right) \right\}\]
\[ = \cos^{- 1} \left\{ \cos\left( \frac{\pi}{3} \right) \right\} + \sin^{- 1} \left\{ - \sin\left( \frac{\pi}{3} \right) \right\}\]
\[ = \cos^{- 1} \left\{ \cos\left( \frac{\pi}{3} \right) \right\} - \sin^{- 1} \left\{ \sin\left( \frac{\pi}{3} \right) \right\}\]
\[ = \frac{\pi}{3} - \frac{\pi}{3}\]
\[ = 0\]
APPEARS IN
संबंधित प्रश्न
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
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.
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
`sin^-1(sin (17pi)/8)`
`sin^-1(sin2)`
Evaluate the following:
`cos^-1{cos ((4pi)/3)}`
Evaluate the following:
`cos^-1(cos4)`
Evaluate the following:
`tan^-1(tan (6pi)/7)`
Evaluate the following:
`tan^-1(tan4)`
Evaluate the following:
`sec^-1(sec (25pi)/6)`
Evaluate the following:
`cot^-1{cot (-(8pi)/3)}`
Write the following in the simplest form:
`tan^-1sqrt((a-x)/(a+x)),-a<x<a`
Evaluate:
`tan{cos^-1(-7/25)}`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x < 0
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
Evaluate the following:
`sin(2tan^-1 2/3)+cos(tan^-1sqrt3)`
If `sin^-1 (2a)/(1+a^2)+sin^-1 (2b)/(1+b^2)=2tan^-1x,` Prove that `x=(a+b)/(1-ab).`
Solve the following equation for x:
`tan^-1((2x)/(1-x^2))+cot^-1((1-x^2)/(2x))=(2pi)/3,x>0`
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
What is the value of cos−1 `(cos (2x)/3)+sin^-1(sin (2x)/3)?`
Write the value of cos−1 (cos 1540°).
Write the value of cos−1 (cos 350°) − sin−1 (sin 350°)
If tan−1 x + tan−1 y = `pi/4`, then write the value of x + y + xy.
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
If \[\sin^{- 1} \left( \frac{1}{3} \right) + \cos^{- 1} x = \frac{\pi}{2},\] then find x.
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Wnte the value of the expression \[\tan\left( \frac{\sin^{- 1} x + \cos^{- 1} x}{2} \right), \text { when } x = \frac{\sqrt{3}}{2}\]
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
sin\[\left[ \cot^{- 1} \left\{ \tan\left( \cos^{- 1} x \right) \right\} \right]\] is equal to
sin \[\left\{ 2 \cos^{- 1} \left( \frac{- 3}{5} \right) \right\}\] is equal to
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
The domain of \[\cos^{- 1} \left( x^2 - 4 \right)\] is
The value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find \[\frac{dy}{dx}\] When \[\theta = \frac{\pi}{3}\] .
