Advertisements
Advertisements
Question
`sin^-1(sin3)`
Advertisements
Solution
We know
`sin(sin^-1theta)=theta if - pi/2<=theta<=pi/2`
We have
`sin^-1(sin3)=sin^-1{sin(pi-3)}`
= π - 3
APPEARS IN
RELATED QUESTIONS
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
Solve the following for x:
`sin^(-1)(1-x)-2sin^-1 x=pi/2`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
`sin^-1(sin pi/6)`
`sin^-1(sin (5pi)/6)`
`sin^-1(sin (13pi)/7)`
`sin^-1(sin (17pi)/8)`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`sec^-1(sec (25pi)/6)`
Evaluate the following:
`cot^-1(cot (4pi)/3)`
Write the following in the simplest form:
`cot^-1 a/sqrt(x^2-a^2),| x | > a`
Write the following in the simplest form:
`tan^-1{sqrt(1+x^2)-x},x in R`
Write the following in the simplest form:
`tan^-1(x/(a+sqrt(a^2-x^2))),-a<x<a`
Evaluate:
`cot(tan^-1a+cot^-1a)`
Find the value of `tan^-1 (x/y)-tan^-1((x-y)/(x+y))`
Solve the following equation for x:
tan−1(x −1) + tan−1x tan−1(x + 1) = tan−13x
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))`
Solve the equation `cos^-1 a/x-cos^-1 b/x=cos^-1 1/b-cos^-1 1/a`
Evaluate the following:
`sin(2tan^-1 2/3)+cos(tan^-1sqrt3)`
`2tan^-1(1/2)+tan^-1(1/7)=tan^-1(31/17)`
Find the value of the following:
`tan^-1{2cos(2sin^-1 1/2)}`
Solve the following equation for x:
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
If x < 0, then write the value of cos−1 `((1-x^2)/(1+x^2))` in terms of tan−1 x.
Write the value of
\[\cos^{- 1} \left( \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\].
Show that \[\sin^{- 1} (2x\sqrt{1 - x^2}) = 2 \sin^{- 1} x\]
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
Write the principal value of \[\cos^{- 1} \left( \cos\frac{2\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{2\pi}{3} \right)\]
Wnte the value of the expression \[\tan\left( \frac{\sin^{- 1} x + \cos^{- 1} x}{2} \right), \text { when } x = \frac{\sqrt{3}}{2}\]
The set of values of `\text(cosec)^-1(sqrt3/2)`
Find the value of \[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right)\]
If x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals
In a ∆ ABC, if C is a right angle, then
\[\tan^{- 1} \left( \frac{a}{b + c} \right) + \tan^{- 1} \left( \frac{b}{c + a} \right) =\]
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 simplified form of `cos^-1 (3/5 cosx + 4/5 sin x)`, where x ∈ `[(-3pi)/4, pi/4]`
The period of the function f(x) = tan3x is ____________.
