Advertisements
Advertisements
प्रश्न
Write the following in the simplest form:
`tan^-1sqrt((a-x)/(a+x)),-a<x<a`
उत्तर
Let `x = acos theta`
Now,
`tan^-1sqrt((a-x)/(a+x))=tan^-1sqrt((a-acostheta)/(a+acostheta))`
`=tan^-1sqrt((1-costheta)/(1+costheta))`
`=tan^-1sqrt((2sin^2 theta/2)/(2cos^2 theta/2))`
`=tan^-1(tan theta/2)`
`=theta/2`
`=1/2cos^-1(x/a)`
`thereforetan^-1sqrt((a-x)/(a+x))=(cos^-1(x/a))/2`
APPEARS IN
संबंधित प्रश्न
Find the principal values of the following:
`cos^-1(-1/sqrt2)`
Find the principal values of the following:
`cos^-1(tan (3pi)/4)`
`sin^-1(sin3)`
`sin^-1(sin2)`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Evaluate the following:
`cosec^-1(cosec (11pi)/6)`
Evaluate the following:
`sin(tan^-1 24/7)`
Solve: `cos(sin^-1x)=1/6`
Evaluate:
`cos(tan^-1 3/4)`
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
If `cot(cos^-1 3/5+sin^-1x)=0`, find the values of x.
Solve the following equation for x:
tan−1(x −1) + tan−1x tan−1(x + 1) = tan−13x
Solve the following equation for x:
`tan^-1 (x-2)/(x-1)+tan^-1 (x+2)/(x+1)=pi/4`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
`tan^-1 1/4+tan^-1 2/9=1/2cos^-1 3/2=1/2sin^-1(4/5)`
`2tan^-1 3/4-tan^-1 17/31=pi/4`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
If `sin^-1x+sin^-1y+sin^-1z=(3pi)/2,` then write the value of x + y + z.
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
Evaluate sin \[\left( \tan^{- 1} \frac{3}{4} \right)\]
If tan−1 x + tan−1 y = `pi/4`, then write the value of x + y + xy.
Write the value of sin−1 \[\left( \cos\frac{\pi}{9} \right)\]
If 4 sin−1 x + cos−1 x = π, then what is the value of x?
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
Write the principal value of \[\cos^{- 1} \left( \cos680^\circ \right)\]
If α = \[\tan^{- 1} \left( \tan\frac{5\pi}{4} \right) \text{ and }\beta = \tan^{- 1} \left( - \tan\frac{2\pi}{3} \right)\] , then
The number of real solutions of the equation \[\sqrt{1 + \cos 2x} = \sqrt{2} \sin^{- 1} (\sin x), - \pi \leq x \leq \pi\]
If \[\cos^{- 1} \frac{x}{2} + \cos^{- 1} \frac{y}{3} = \theta,\] then 9x2 − 12xy cos θ + 4y2 is equal to
If tan−1 3 + tan−1 x = tan−1 8, then x =
If θ = sin−1 {sin (−600°)}, then one of the possible values of θ is
If \[3\sin^{- 1} \left( \frac{2x}{1 + x^2} \right) - 4 \cos^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) + 2 \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) = \frac{\pi}{3}\] is equal to
The value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
tanx is periodic with period ____________.
