Advertisements
Advertisements
प्रश्न
Evaluate the following:
`sin(sec^-1 17/8)`
Advertisements
उत्तर
`=sin(sec^-1 17/8)=sin(cos^-1 8/17)`
`=sin[sin^-1sqrt(1-(8/17)^2)]` `[thereforecos^-1x=sin^-1sqrt(1-x^2)]`
`=sin[sin^-1(sqrt(1-64/289))]`
`=sin[sin^-1(sqrt(225/289))]`
`=sin[sin^-1 15/17]`
`=15/17`
APPEARS IN
संबंधित प्रश्न
If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy.
`sin^-1(sin (5pi)/6)`
`sin^-1(sin12)`
Evaluate the following:
`cos^-1(cos4)`
Evaluate the following:
`sec^-1(sec pi/3)`
Evaluate the following:
`sec^-1(sec (7pi)/3)`
Evaluate the following:
`sec^-1(sec (13pi)/4)`
Evaluate the following:
`cosec^-1(cosec (13pi)/6)`
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)+1)/x},x !=0`
Write the following in the simplest form:
`tan^-1sqrt((a-x)/(a+x)),-a<x<a`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Evaluate the following:
`sin(sin^-1 7/25)`
Evaluate the following:
`tan(cos^-1 8/17)`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
`sin^-1x=pi/6+cos^-1x`
`tan^-1 1/7+2tan^-1 1/3=pi/4`
`2sin^-1 3/5-tan^-1 17/31=pi/4`
Find the value of the following:
`cos(sec^-1x+\text(cosec)^-1x),` | x | ≥ 1
Solve the following equation for x:
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
Write the difference between maximum and minimum values of sin−1 x for x ∈ [− 1, 1].
If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.
Write the value of
\[\cos^{- 1} \left( \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\].
If \[\sin^{- 1} \left( \frac{1}{3} \right) + \cos^{- 1} x = \frac{\pi}{2},\] then find x.
Write the value of \[\sin^{- 1} \left( \frac{1}{3} \right) - \cos^{- 1} \left( - \frac{1}{3} \right)\]
Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`
The set of values of `\text(cosec)^-1(sqrt3/2)`
Write the value of \[\tan^{- 1} \left( \frac{1}{x} \right)\] for x < 0 in terms of `cot^-1x`
If x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals
The value of \[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right)\] is
If \[\cos^{- 1} x > \sin^{- 1} x\], then
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
The domain of \[\cos^{- 1} \left( x^2 - 4 \right)\] is
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
Prove that : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
Prove that : \[\cot^{- 1} \frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}} = \frac{x}{2}, 0 < x < \frac{\pi}{2}\] .
Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
