Advertisements
Advertisements
प्रश्न
`2tan^-1 1/5+tan^-1 1/8=tan^-1 4/7`
उत्तर
LHS = `2tan^-1 1/5+tan^-1 1/8`
`=tan^-1{(2xx1/5)/(1-(1/5)^2)}+tan^-1 1/8` `[because2tan^-1x=tan^-1{(2x)/(1-x^2)}]`
`=tan^-1{(2/5)/(24/25)}+tan^-1 1/8`
`=tan^-1 5/12+tan^-1 1/8`
`=tan^-1((5/12+1/8)/(1-5/12xx1/8))` `[becausetan^-1x+tan^-1y=tan^-1((x+y)/(1-xy))]`
`=tan^-1((13/24)/(91/96))`
`=tan^-1 4/7`= RHS
APPEARS IN
संबंधित प्रश्न
Write the value of `tan(2tan^(-1)(1/5))`
Find the value of the following: `tan(1/2)[sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))],|x| <1,y>0 and xy <1`
If `(sin^-1x)^2 + (sin^-1y)^2+(sin^-1z)^2=3/4pi^2,` find the value of x2 + y2 + z2
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
Find the principal values of the following:
`cos^-1(tan (3pi)/4)`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`tan^-1(tan (7pi)/6)`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Evaluate the following:
`cot^-1{cot (-(8pi)/3)}`
Write the following in the simplest form:
`tan^-1{sqrt(1+x^2)-x},x in R `
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{(sqrt(1+x)+sqrt(1-x))/2},0<x<1`
Evaluate the following:
`sin(tan^-1 24/7)`
Evaluate:
`cot{sec^-1(-13/5)}`
`sin^-1x=pi/6+cos^-1x`
Solve the following equation for x:
tan−1(x + 2) + tan−1(x − 2) = tan−1 `(8/79)`, x > 0
Solve the following equation for x:
`tan^-1 (x-2)/(x-1)+tan^-1 (x+2)/(x+1)=pi/4`
Sum the following series:
`tan^-1 1/3+tan^-1 2/9+tan^-1 4/33+...+tan^-1 (2^(n-1))/(1+2^(2n-1))`
If `cos^-1 x/2+cos^-1 y/3=alpha,` then prove that `9x^2-12xy cosa+4y^2=36sin^2a.`
Solve the equation `cos^-1 a/x-cos^-1 b/x=cos^-1 1/b-cos^-1 1/a`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
Solve the following equation for x:
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.
If −1 < x < 0, then write the value of `sin^-1((2x)/(1+x^2))+cos^-1((1-x^2)/(1+x^2))`
Evaluate sin
\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the value of \[\sec^{- 1} \left( \frac{1}{2} \right)\]
Write the value of \[\tan^{- 1} \left( \frac{1}{x} \right)\] for x < 0 in terms of `cot^-1x`
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
Find the value of \[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right)\]
The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is
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 4 cos−1 x + sin−1 x = π, then the value of x is
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find \[\frac{dy}{dx}\] When \[\theta = \frac{\pi}{3}\] .
