Advertisements
Advertisements
प्रश्न
Evaluate the following:
`cos^-1(cos12)`
Advertisements
उत्तर
We know
`cos^-1(costheta)=thetaif 0<=theta<=pi`
We have
`cos^-1(cos12)=cos^-1{cos(4pi-12)}`
= 4π - 12
APPEARS IN
संबंधित प्रश्न
Write the value of `tan(2tan^(-1)(1/5))`
Find the value of the following: `tan(1/2)[sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))],|x| <1,y>0 and xy <1`
If (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
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 (7pi)/6)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`tan^-1(tan (9pi)/4)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Write the following in the simplest form:
`tan^-1{x+sqrt(1+x^2)},x in R `
Evaluate the following:
`sin(sin^-1 7/25)`
Evaluate the following:
`sin(sec^-1 17/8)`
Evaluate the following:
`sec(sin^-1 12/13)`
Evaluate:
`sec{cot^-1(-5/12)}`
Evaluate:
`cosec{cot^-1(-12/5)}`
If `sin^-1x+sin^-1y=pi/3` and `cos^-1x-cos^-1y=pi/6`, find the values of x and y.
Solve the following equation for x:
tan−1(x + 1) + tan−1(x − 1) = tan−1`8/31`
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
Solve `cos^-1sqrt3x+cos^-1x=pi/2`
`sin^-1 4/5+2tan^-1 1/3=pi/2`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
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 (cos 1540°).
Write the value of cos−1 \[\left( \cos\frac{5\pi}{4} \right)\]
If \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find 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 value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is
If sin−1 x − cos−1 x = `pi/6` , then x =
If 4 cos−1 x + sin−1 x = π, then the value of x is
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
Prove that : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
Write the value of \[\cos^{- 1} \left( - \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\] .
Find the domain of `sec^(-1)(3x-1)`.
