Advertisements
Advertisements
प्रश्न
`sin^-1(sin (13pi)/7)`
Advertisements
उत्तर
We know
`sin(sin^-1theta)=theta if - pi/2<=theta<=pi/2`
We have
`sin^-1(sin (13pi)/7)=sin^-1{sin(2pi+pi/7)}`
`=sin^-1(sin-pi/7)`
`=-pi/7`
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 for x:
`2tan^(-1)(cosx)=tan^(-1)(2"cosec" x)`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
Find the principal values of the following:
`cos^-1(-1/sqrt2)`
`sin^-1(sin4)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`tan^-1(tan (6pi)/7)`
Evaluate the following:
`sec^-1{sec (-(7pi)/3)}`
Evaluate the following:
`sin(tan^-1 24/7)`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Solve: `cos(sin^-1x)=1/6`
`5tan^-1x+3cot^-1x=2x`
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
Evaluate the following:
`tan 1/2(cos^-1 sqrt5/3)`
`tan^-1 2/3=1/2tan^-1 12/5`
`2tan^-1 1/5+tan^-1 1/8=tan^-1 4/7`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
Solve the following equation for x:
`tan^-1 1/4+2tan^-1 1/5+tan^-1 1/6+tan^-1 1/x=pi/4`
Solve the following equation for x:
`tan^-1((2x)/(1-x^2))+cot^-1((1-x^2)/(2x))=(2pi)/3,x>0`
Write the value of sin (cot−1 x).
Write the value of
\[\cos^{- 1} \left( \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\].
Write the value of sin−1
\[\left( \sin( -{600}°) \right)\].
Evaluate sin
\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]
Write the value of cos−1 \[\left( \tan\frac{3\pi}{4} \right)\]
Write the value of cos−1 \[\left( \cos\frac{5\pi}{4} \right)\]
Write the principal value of \[\cos^{- 1} \left( \cos\frac{2\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{2\pi}{3} \right)\]
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
Write the value of \[\sec^{- 1} \left( \frac{1}{2} \right)\]
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
Find the value of \[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right)\]
The number of solutions of the equation \[\tan^{- 1} 2x + \tan^{- 1} 3x = \frac{\pi}{4}\] is
Let f (x) = `e^(cos^-1){sin(x+pi/3}.`
Then, f (8π/9) =
If x > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to
Find the domain of `sec^(-1)(3x-1)`.
Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
The period of the function f(x) = tan3x is ____________.
