Advertisements
Advertisements
प्रश्न
Evaluate the following:
`cot(cos^-1 3/5)`
Advertisements
उत्तर
`cot(cos^-1 3/5)=cot{tan^-1 sqrt(1-(3/5)^2)/(3/5)}` `[thereforecos^-1x=tan^-1 (sqrt(1-z^2)/x)]`
`=cot(tan^-1 (4/5)/(8/17))`
`=cot(cot^-1 3/4)`
`=3/4`
APPEARS IN
संबंधित प्रश्न
Prove that
`tan^(-1) [(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))]=pi/4-1/2 cos^(-1)x,-1/sqrt2<=x<=1`
If `(sin^-1x)^2 + (sin^-1y)^2+(sin^-1z)^2=3/4pi^2,` find the value of x2 + y2 + z2
Find the domain of `f(x)=cos^-1x+cosx.`
`sin^-1(sin pi/6)`
`sin^-1(sin2)`
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Evaluate the following:
`tan^-1(tan12)`
Evaluate the following:
`cot^-1(cot (9pi)/4)`
Evaluate the following:
`sin(sin^-1 7/25)`
Evaluate the following:
`sec(sin^-1 12/13)`
Solve: `cos(sin^-1x)=1/6`
Evaluate:
`cot{sec^-1(-13/5)}`
Evaluate:
`cos(tan^-1 3/4)`
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
Solve the following equation for x:
`tan^-1 (x-2)/(x-1)+tan^-1 (x+2)/(x+1)=pi/4`
Sum the following series:
`tan^-1 1/3+tan^-1 2/9+tan^-1 4/33+...+tan^-1 (2^(n-1))/(1+2^(2n-1))`
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
`(9pi)/8-9/4sin^-1 1/3=9/4sin^-1 (2sqrt2)/3`
`2tan^-1 3/4-tan^-1 17/31=pi/4`
Find the value of the following:
`cos(sec^-1x+\text(cosec)^-1x),` | x | ≥ 1
If `sin^-1x+sin^-1y+sin^-1z=(3pi)/2,` then write the value of x + y + z.
Write the value of tan−1 x + tan−1 `(1/x)` for x < 0.
What is the value of cos−1 `(cos (2x)/3)+sin^-1(sin (2x)/3)?`
Write the range of tan−1 x.
If tan−1 x + tan−1 y = `pi/4`, then write the value of x + y + xy.
If \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find x.
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
Wnte the value of\[\cos\left( \frac{\tan^{- 1} x + \cot^{- 1} x}{3} \right), \text{ when } x = - \frac{1}{\sqrt{3}}\]
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
If \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} - \sqrt{1 - x^2}}{\sqrt{1 + x^2} + \sqrt{1 - x^2}} \right)\] = α, then x2 =
The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is
If x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
The value of tan `("cos"^-1 4/5 + "tan"^-1 2/3) =`
