Advertisements
Advertisements
प्रश्न
What is the principal value of `sin^-1(-sqrt3/2)?`
उत्तर
Let `y=sin^-1(-sqrt3/2)`
Then,
\[\sin{y} = - \frac{\sqrt{3}}{2} = \sin\left( - \frac{\pi}{3} \right)\]
\[y = - \frac{\pi}{3} \in \left[ - \frac{\pi}{2}, \frac{\pi}{2} \right]\]
Here
\[\left[ - \frac{\pi}{2}, \frac{\pi}{2} \right]\] is the range of the principal value branch of inverse sine function.
∴ `sin^-1(-sqrt3/2)=-pi/3`
APPEARS IN
संबंधित प्रश्न
Write the value of `tan(2tan^(-1)(1/5))`
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`
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
`sin^-1(sin (13pi)/7)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`tan^-1(tan (6pi)/7)`
Evaluate the following:
`tan^-1(tan2)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Evaluate the following:
`cosec^-1(cosec (11pi)/6)`
Evaluate the following:
`cosec^-1{cosec (-(9pi)/4)}`
Evaluate the following:
`cot^-1(cot (19pi)/6)`
Write the following in the simplest form:
`cot^-1 a/sqrt(x^2-a^2),| x | > a`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Evaluate the following:
`sin(cos^-1 5/13)`
Evaluate the following:
`cos(tan^-1 24/7)`
Evaluate:
`tan{cos^-1(-7/25)}`
Evaluate:
`cos(tan^-1 3/4)`
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
`sin^-1x=pi/6+cos^-1x`
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−1x tan−1(x + 1) = tan−13x
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
If `cos^-1 x/2+cos^-1 y/3=alpha,` then prove that `9x^2-12xy cosa+4y^2=36sin^2a.`
Evaluate the following:
`tan 1/2(cos^-1 sqrt5/3)`
`2tan^-1(1/2)+tan^-1(1/7)=tan^-1(31/17)`
Show that `2tan^-1x+sin^-1 (2x)/(1+x^2)` is constant for x ≥ 1, find that constant.
Solve the following equation for x:
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
If −1 < x < 0, then write the value of `sin^-1((2x)/(1+x^2))+cos^-1((1-x^2)/(1+x^2))`
If 4 sin−1 x + cos−1 x = π, then what is the value of x?
Wnte the value of the expression \[\tan\left( \frac{\sin^{- 1} x + \cos^{- 1} x}{2} \right), \text { when } x = \frac{\sqrt{3}}{2}\]
If \[\cos^{- 1} \frac{x}{a} + \cos^{- 1} \frac{y}{b} = \alpha, then\frac{x^2}{a^2} - \frac{2xy}{ab}\cos \alpha + \frac{y^2}{b^2} = \]
If x > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to
If y = sin (sin x), prove that \[\frac{d^2 y}{d x^2} + \tan x \frac{dy}{dx} + y \cos^2 x = 0 .\]
Write the value of \[\cos^{- 1} \left( - \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\] .
The equation sin-1 x – cos-1 x = cos-1 `(sqrt3/2)` has ____________.
