Advertisements
Advertisements
प्रश्न
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
Advertisements
उत्तर
Let sec-1 `(1/x) = theta`
` ⇒ sec theta = 1/x`
⇒ cos θ = x
⇒ tan ` (sec^(-1) (1/x)) = tan theta = sqrt(1 -x^2 ) /x ` ...(1)
Now consider,
sin ( tan -1 2 )
Let tan-1 2 = Φ
tan Φ = 2
sin ( tan-1 2) = sin Φ = `2/sqrt(5) ` ...(ii)
From (i) and (ii)
`sqrt(1- x^2 )/x = 2/sqrt(5)`
5(1 - x2 ) = 4x2
`x = +- sqrt(5)/3 " but " x > 0 ⇒ x = sqrt(5)/3`
APPEARS IN
संबंधित प्रश्न
Solve the equation for x:sin−1x+sin−1(1−x)=cos−1x
If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy.
Find the principal values of the following:
`cos^-1(tan (3pi)/4)`
`sin^-1(sin (17pi)/8)`
`sin^-1(sin3)`
`sin^-1(sin4)`
Evaluate the following:
`cos^-1(cos5)`
Evaluate the following:
`tan^-1(tan (9pi)/4)`
Evaluate the following:
`sec^-1(sec (5pi)/4)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Evaluate:
`cos(tan^-1 3/4)`
Solve the following equation for x:
tan−1(x −1) + tan−1x tan−1(x + 1) = tan−13x
Solve the equation `cos^-1 a/x-cos^-1 b/x=cos^-1 1/b-cos^-1 1/a`
`2tan^-1 1/5+tan^-1 1/8=tan^-1 4/7`
Solve the following equation for x:
`tan^-1((2x)/(1-x^2))+cot^-1((1-x^2)/(2x))=(2pi)/3,x>0`
Write the difference between maximum and minimum values of sin−1 x for x ∈ [− 1, 1].
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 cos2 \[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
What is the principal value of `sin^-1(-sqrt3/2)?`
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 \[2 \sec^{- 1} 2 + \sin^{- 1} \left( \frac{1}{2} \right)\]
Let f (x) = `e^(cos^-1){sin(x+pi/3}.`
Then, f (8π/9) =
If \[\cos^{- 1} x > \sin^{- 1} x\], then
The value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]
Solve for x : {xcos(cot-1 x) + sin(cot-1 x)}2 = `51/50`
