Advertisements
Advertisements
प्रश्न
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
उत्तर
We have
\[\left| x \right| \leq 1\]
\[ \Rightarrow \pm x \leq 1\]
\[ \Rightarrow x \leq 1 or - x \leq 1\]
\[ \Rightarrow x \leq 1 or x \geq - 1\]
\[ \Rightarrow x \in \left[ - 1, 1 \right]\]
Now,
\[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right) = \cos\left( \frac{\pi}{2} \right) \left[ \because \sin^{- 1} x + \cos^{- 1} x = \frac{\pi}{2} \right]\]
\[ = 0\]
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`
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
If `tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4` ,find the value of x
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
`sin^-1(sin (17pi)/8)`
`sin^-1(sin3)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`cot^-1(cot (4pi)/3)`
Write the following in the simplest form:
`tan^-1{x+sqrt(1+x^2)},x in R `
Write the following in the simplest form:
`tan^-1(x/(a+sqrt(a^2-x^2))),-a<x<a`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Evaluate the following:
`sin(sec^-1 17/8)`
Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x < 0
If `(sin^-1x)^2+(cos^-1x)^2=(17pi^2)/36,` Find x
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
Evaluate the following:
`tan{2tan^-1 1/5-pi/4}`
Prove that:
`2sin^-1 3/5=tan^-1 24/7`
`2sin^-1 3/5-tan^-1 17/31=pi/4`
`2tan^-1 1/5+tan^-1 1/8=tan^-1 4/7`
`2tan^-1 3/4-tan^-1 17/31=pi/4`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
Find the value of the following:
`cos(sec^-1x+\text(cosec)^-1x),` | x | ≥ 1
Solve the following equation for x:
`tan^-1((2x)/(1-x^2))+cot^-1((1-x^2)/(2x))=(2pi)/3,x>0`
For any a, b, x, y > 0, prove that:
`2/3tan^-1((3ab^2-a^3)/(b^3-3a^2b))+2/3tan^-1((3xy^2-x^3)/(y^3-3x^2y))=tan^-1 (2alphabeta)/(alpha^2-beta^2)`
`where alpha =-ax+by, beta=bx+ay`
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
Write the value of tan−1 x + tan−1 `(1/x)` for x < 0.
Show that \[\sin^{- 1} (2x\sqrt{1 - x^2}) = 2 \sin^{- 1} x\]
If \[\sin^{- 1} \left( \frac{1}{3} \right) + \cos^{- 1} x = \frac{\pi}{2},\] then find x.
Write the value of \[\sec^{- 1} \left( \frac{1}{2} \right)\]
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
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] is equal to
If \[\cos^{- 1} \frac{x}{2} + \cos^{- 1} \frac{y}{3} = \theta,\] then 9x2 − 12xy cos θ + 4y2 is equal to
\[\cot\left( \frac{\pi}{4} - 2 \cot^{- 1} 3 \right) =\]
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find \[\frac{dy}{dx}\] When \[\theta = \frac{\pi}{3}\] .
Find the domain of `sec^(-1)(3x-1)`.
The period of the function f(x) = tan3x is ____________.
