Advertisements
Advertisements
Question
What is the value of cos−1 `(cos (2x)/3)+sin^-1(sin (2x)/3)?`
Solution
`cos^-1(cos (2x)/3)+sin^-1(sin (2x)/3)`
`cos^-1(cos (2x)/3)+sin^-1{sin(pi/3)}` `[because "Range of sine is"[-pi/2, pi/2]; pi/3in [-pi/2,pi/2] "and range of cosine is" [0,pi] ; (2pi)/3in [0, pi]]`
`=(2pi)/3+pi/3`
= π
APPEARS IN
RELATED QUESTIONS
Write the value of `tan(2tan^(-1)(1/5))`
Prove that :
`2 tan^-1 (sqrt((a-b)/(a+b))tan(x/2))=cos^-1 ((a cos x+b)/(a+b cosx))`
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
`sin^-1(sin pi/6)`
`sin^-1(sin (13pi)/7)`
`sin^-1(sin (17pi)/8)`
`sin^-1(sin3)`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
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:
`tan^-1sqrt((a-x)/(a+x)),-a<x<a`
Evaluate the following:
`sin(tan^-1 24/7)`
Evaluate the following:
`cot(cos^-1 3/5)`
Evaluate the following:
`cos(tan^-1 24/7)`
Prove the following result-
`tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5`
Solve: `cos(sin^-1x)=1/6`
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
Solve the equation `cos^-1 a/x-cos^-1 b/x=cos^-1 1/b-cos^-1 1/a`
`tan^-1 1/7+2tan^-1 1/3=pi/4`
`2tan^-1 3/4-tan^-1 17/31=pi/4`
If `sin^-1 (2a)/(1+a^2)+sin^-1 (2b)/(1+b^2)=2tan^-1x,` Prove that `x=(a+b)/(1-ab).`
Solve the following equation for x:
`tan^-1((2x)/(1-x^2))+cot^-1((1-x^2)/(2x))=(2pi)/3,x>0`
Solve the following equation for x:
`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`
Prove that:
`tan^-1 (2ab)/(a^2-b^2)+tan^-1 (2xy)/(x^2-y^2)=tan^-1 (2alphabeta)/(alpha^2-beta^2),` where `alpha=ax-by and beta=ay+bx.`
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`
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 tan−1x + tan−1 `(1/x)`for x > 0.
Write the value of sin−1
\[\left( \sin( -{600}°) \right)\].
Evaluate sin
\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]
If tan−1 x + tan−1 y = `pi/4`, then write the value of x + y + xy.
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
Find the value of \[2 \sec^{- 1} 2 + \sin^{- 1} \left( \frac{1}{2} \right)\]
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] is equal to
If θ = sin−1 {sin (−600°)}, then one of the possible values of θ is
\[\cot\left( \frac{\pi}{4} - 2 \cot^{- 1} 3 \right) =\]
The period of the function f(x) = tan3x is ____________.
Find the value of `sin^-1(cos((33π)/5))`.
