Advertisements
Advertisements
प्रश्न
Solve the following equation for x:
`tan^-1((1-x)/(1+x))-1/2 tan^-1x` = 0, where x > 0
Advertisements
उत्तर
`tan^-1((1-x)/(1+x))-1/2 tan^-1x` = 0
⇒ `tan^-1((1-x)/(1+x))=1/2tan^-1(x)`
⇒ `tan^-1 1-tan^-1x=1/2tan^-1(x)`
⇒ `tan^-1 1=3/2tan^-1(x)`
⇒ `pi/4=3/2tan^-1(x)`
⇒ `pi/6=tan^-1(x)`
⇒ `x=1/sqrt3`
संबंधित प्रश्न
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 `(sin^-1x)^2 + (sin^-1y)^2+(sin^-1z)^2=3/4pi^2,` find the value of x2 + y2 + z2
`sin^-1(sin pi/6)`
`sin^-1(sin (17pi)/8)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`tan^-1(tan pi/3)`
Evaluate the following:
`sec^-1(sec pi/3)`
Evaluate the following:
`cot^-1(cot pi/3)`
Evaluate the following:
`cot^-1{cot ((21pi)/4)}`
Solve: `cos(sin^-1x)=1/6`
Evaluate:
`cot{sec^-1(-13/5)}`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x < 0
`4sin^-1x=pi-cos^-1x`
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
If `cos^-1 x/2+cos^-1 y/3=alpha,` then prove that `9x^2-12xy cosa+4y^2=36sin^2a.`
`tan^-1 1/4+tan^-1 2/9=1/2cos^-1 3/2=1/2sin^-1(4/5)`
`2sin^-1 3/5-tan^-1 17/31=pi/4`
`2tan^-1 3/4-tan^-1 17/31=pi/4`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
If `sin^-1 (2a)/(1+a^2)-cos^-1 (1-b^2)/(1+b^2)=tan^-1 (2x)/(1-x^2)`, then prove that `x=(a-b)/(1+ab)`
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=pi/2`
If `sin^-1x+sin^-1y+sin^-1z=(3pi)/2,` then write the value of x + y + z.
Write the value of tan−1 x + tan−1 `(1/x)` for x < 0.
Write the value of sin−1 (sin 1550°).
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
If \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find x.
If 4 sin−1 x + cos−1 x = π, then what is the value of x?
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
If α = \[\tan^{- 1} \left( \frac{\sqrt{3}x}{2y - x} \right), \beta = \tan^{- 1} \left( \frac{2x - y}{\sqrt{3}y} \right),\]
then α − β =
Let f (x) = `e^(cos^-1){sin(x+pi/3}.`
Then, f (8π/9) =
The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is
tanx is periodic with period ____________.
Find the value of `sin^-1(cos((33π)/5))`.
