Advertisements
Advertisements
प्रश्न
`(9pi)/8-9/4sin^-1 1/3=9/4sin^-1 (2sqrt2)/3`
उत्तर
`(9pi)/8-9/4sin^-1 1/3=9/4sin^-1 (2sqrt2)/3`
LHS = `(9pi)/8-9/4sin^-1 1/3`
`=9/4(pi/2-sin^-1 1/3)`
`=9/4(cos^-1 1/3)`
`=9/4(sin^-1sqrt(1-1/9))`
`=9/4(sin^-1 (2sqrt2)/3)=` RHS
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`
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
Find the domain of `f(x)=cos^-1x+cosx.`
Find the principal values of the following:
`cos^-1(tan (3pi)/4)`
`sin^-1(sin pi/6)`
`sin^-1(sin (17pi)/8)`
Evaluate the following:
`sec^-1(sec (25pi)/6)`
Evaluate the following:
`\text(cosec)^-1(\text{cosec} pi/4)`
Evaluate the following:
`cosec^-1(cosec (13pi)/6)`
Evaluate the following:
`sin(sin^-1 7/25)`
Evaluate the following:
`cos(tan^-1 24/7)`
Evaluate:
`tan{cos^-1(-7/25)}`
Evaluate:
`cosec{cot^-1(-12/5)}`
Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x > 0
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
Solve the following equation for x:
`tan^-1 2x+tan^-1 3x = npi+(3pi)/4`
Solve the following equation for x:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
Solve the following equation for x:
`tan^-1((x-2)/(x-4))+tan^-1((x+2)/(x+4))=pi/4`
Evaluate the following:
`sin(1/2cos^-1 4/5)`
`tan^-1 1/7+2tan^-1 1/3=pi/4`
Solve the following equation for x:
`2tan^-1(sinx)=tan^-1(2sinx),x!=pi/2`
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.`
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
Write the value of sin (cot−1 x).
Write the value of sin−1
\[\left( \sin( -{600}°) \right)\].
Write the value of cos−1 (cos 350°) − sin−1 (sin 350°)
If tan−1 x + tan−1 y = `pi/4`, then write the value of x + y + xy.
Write the principal value of `sin^-1(-1/2)`
Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
Wnte the value of\[\cos\left( \frac{\tan^{- 1} x + \cot^{- 1} x}{3} \right), \text{ when } x = - \frac{1}{\sqrt{3}}\]
Find the value of \[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right)\]
The positive integral solution of the equation
\[\tan^{- 1} x + \cos^{- 1} \frac{y}{\sqrt{1 + y^2}} = \sin^{- 1} \frac{3}{\sqrt{10}}\text{ is }\]
The number of solutions of the equation \[\tan^{- 1} 2x + \tan^{- 1} 3x = \frac{\pi}{4}\] is
If x > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
