Advertisements
Advertisements
प्रश्न
Evaluate the following:
`tan(cos^-1 8/17)`
उत्तर
`tan(cos^-1 8/17)=tan{tan^-1 (sqrt(1-(8/17)^2))/(8/17)}` `[thereforecos^-1x=tan^-1 ((sqrt(1-x^2))/x)]`
`=tan(tan^-1 (15/17)/(8/17))`
`=15/8`
APPEARS IN
संबंधित प्रश्न
Solve the equation for x:sin−1x+sin−1(1−x)=cos−1x
If `cos^-1( x/a) +cos^-1 (y/b)=alpha` , prove that `x^2/a^2-2(xy)/(ab) cos alpha +y^2/b^2=sin^2alpha`
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
`sin^-1(sin12)`
`sin^-1(sin2)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`cos^-1{cos ((4pi)/3)}`
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Evaluate the following:
`tan^-1(tan4)`
Evaluate the following:
`\text(cosec)^-1(\text{cosec} pi/4)`
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)+1)/x},x !=0`
Write the following in the simplest form:
`sin^-1{(sqrt(1+x)+sqrt(1-x))/2},0<x<1`
Evaluate the following:
`sin(sin^-1 7/25)`
Evaluate the following:
`sin(tan^-1 24/7)`
Evaluate the following:
`cot(cos^-1 3/5)`
Prove the following result
`tan(cos^-1 4/5+tan^-1 2/3)=17/6`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x < 0
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`
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
Solve the following equation for x:
`tan^-1 2x+tan^-1 3x = npi+(3pi)/4`
Solve the following equation for x:
tan−1(x + 1) + tan−1(x − 1) = tan−1`8/31`
Evaluate the following:
`tan 1/2(cos^-1 sqrt5/3)`
`tan^-1 2/3=1/2tan^-1 12/5`
Solve the following equation for x:
`tan^-1 1/4+2tan^-1 1/5+tan^-1 1/6+tan^-1 1/x=pi/4`
If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
Write the value of cos−1 (cos 1540°).
Write the value of \[\sin^{- 1} \left( \frac{1}{3} \right) - \cos^{- 1} \left( - \frac{1}{3} \right)\]
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 \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
If \[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\] , find the value of x.
2 tan−1 {cosec (tan−1 x) − tan (cot−1 x)} is equal to
The positive integral solution of the equation
\[\tan^{- 1} x + \cos^{- 1} \frac{y}{\sqrt{1 + y^2}} = \sin^{- 1} \frac{3}{\sqrt{10}}\text{ is }\]
The value of \[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right)\] is
If θ = sin−1 {sin (−600°)}, then one of the possible values of θ is
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
tanx is periodic with period ____________.
