Advertisements
Advertisements
प्रश्न
Write the following in the simplest form:
`tan^-1(x/(a+sqrt(a^2-x^2))),-a<x<a`
Advertisements
उत्तर
Let `x = asintheta`
Now,
`tan^-1{x/(a+sqrt(a^2-x^2))}=tan^-1{(asintheta)/(a+sqrt(a^2-a^2cos^2theta))}`
`=tan^-1{(asintheta)/(a+asqrt(cos^2theta))}`
`=tan^-1{sintheta/(1+costheta)}`
`=tan^-1{(2sin(theta/2)cos(theta/2))/(2cos^2 theta/2)}`
`=tan^-1{tan theta/2}`
`=theta/2`
`=1/2sin^-1(x/a)`
APPEARS IN
संबंधित प्रश्न
If (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy.
Prove that
`tan^(-1) [(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))]=pi/4-1/2 cos^(-1)x,-1/sqrt2<=x<=1`
If `tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4` ,find the value of x
Find the domain of `f(x)=cos^-1x+cosx.`
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
`sin^-1(sin2)`
Evaluate the following:
`tan^-1(tan (9pi)/4)`
Evaluate the following:
`sec^-1(sec pi/3)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Evaluate the following:
`sec^-1(sec (13pi)/4)`
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:
`sin(sec^-1 17/8)`
Evaluate the following:
`tan(cos^-1 8/17)`
Evaluate:
`cot{sec^-1(-13/5)}`
Evaluate:
`cosec{cot^-1(-12/5)}`
Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`
`sin^-1x=pi/6+cos^-1x`
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(2+x)+tan^-1(2-x)=tan^-1 2/3, where x< -sqrt3 or, x>sqrt3`
`sin^-1 63/65=sin^-1 5/13+cos^-1 3/5`
Evaluate the following:
`sin(1/2cos^-1 4/5)`
`tan^-1 1/4+tan^-1 2/9=1/2cos^-1 3/2=1/2sin^-1(4/5)`
`sin^-1 4/5+2tan^-1 1/3=pi/2`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
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.`
If −1 < x < 0, then write the value of `sin^-1((2x)/(1+x^2))+cos^-1((1-x^2)/(1+x^2))`
Write the value of
\[\cos^{- 1} \left( \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\].
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
Wnte the value of the expression \[\tan\left( \frac{\sin^{- 1} x + \cos^{- 1} x}{2} \right), \text { when } x = \frac{\sqrt{3}}{2}\]
Find the value of \[2 \sec^{- 1} 2 + \sin^{- 1} \left( \frac{1}{2} \right)\]
If sin−1 x − cos−1 x = `pi/6` , then x =
sin \[\left\{ 2 \cos^{- 1} \left( \frac{- 3}{5} \right) \right\}\] is equal to
If 4 cos−1 x + sin−1 x = π, then the value of x is
The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] is
If \[\sin^{- 1} \left( \frac{2a}{1 - a^2} \right) + \cos^{- 1} \left( \frac{1 - a^2}{1 + a^2} \right) = \tan^{- 1} \left( \frac{2x}{1 - x^2} \right),\text{ where }a, x \in \left( 0, 1 \right)\] , then, the value of x is
The domain of \[\cos^{- 1} \left( x^2 - 4 \right)\] is
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find \[\frac{dy}{dx}\] When \[\theta = \frac{\pi}{3}\] .
The value of sin `["cos"^-1 (7/25)]` is ____________.
