Advertisements
Advertisements
प्रश्न
Find the value of the following:
`cos(sec^-1x+\text(cosec)^-1x),` | x | ≥ 1
Advertisements
उत्तर
We have
`cos(sec^-1x+\text(cosec)^-1x)`
`=cos pi/2` `[becausesec^-1x+\text(cosec)^-1x=pi/2]`
= 0
`thereforecos(sec^-1x+\text(cosec)^-1x)=0` , ∣ x ∣ ≥1
APPEARS IN
संबंधित प्रश्न
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 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
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
`sin^-1(sin2)`
Evaluate the following:
`cos^-1(cos4)`
Evaluate the following:
`sec^-1(sec (25pi)/6)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`cosec^-1(cosec (11pi)/6)`
Evaluate the following:
`cosec^-1{cosec (-(9pi)/4)}`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Evaluate the following:
`cot(cos^-1 3/5)`
Prove the following result
`tan(cos^-1 4/5+tan^-1 2/3)=17/6`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
Prove the following result:
`tan^-1 1/4+tan^-1 2/9=sin^-1 1/sqrt5`
Evaluate the following:
`tan 1/2(cos^-1 sqrt5/3)`
`2tan^-1 1/5+tan^-1 1/8=tan^-1 4/7`
Prove that
`sin{tan^-1 (1-x^2)/(2x)+cos^-1 (1-x^2)/(2x)}=1`
Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
Write the value of sin (cot−1 x).
Write the value of sin−1
\[\left( \sin( -{600}°) \right)\].
Evaluate sin \[\left( \tan^{- 1} \frac{3}{4} \right)\]
Write the value of sin−1 \[\left( \cos\frac{\pi}{9} \right)\]
Write the value of sin \[\left\{ \frac{\pi}{3} - \sin^{- 1} \left( - \frac{1}{2} \right) \right\}\]
If \[\sin^{- 1} \left( \frac{1}{3} \right) + \cos^{- 1} x = \frac{\pi}{2},\] then find x.
Write the principal value of \[\sin^{- 1} \left\{ \cos\left( \sin^{- 1} \frac{1}{2} \right) \right\}\]
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is
The positive integral solution of the equation
\[\tan^{- 1} x + \cos^{- 1} \frac{y}{\sqrt{1 + y^2}} = \sin^{- 1} \frac{3}{\sqrt{10}}\text{ is }\]
Let f (x) = `e^(cos^-1){sin(x+pi/3}.`
Then, f (8π/9) =
It \[\tan^{- 1} \frac{x + 1}{x - 1} + \tan^{- 1} \frac{x - 1}{x} = \tan^{- 1}\] (−7), then the value of x is
If tan−1 (cot θ) = 2 θ, then θ =
The domain of \[\cos^{- 1} \left( x^2 - 4 \right)\] is
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find \[\frac{dy}{dx}\] When \[\theta = \frac{\pi}{3}\] .
If y = sin (sin x), prove that \[\frac{d^2 y}{d x^2} + \tan x \frac{dy}{dx} + y \cos^2 x = 0 .\]
Find the domain of `sec^(-1)(3x-1)`.
Find the domain of `sec^(-1) x-tan^(-1)x`
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
