Advertisements
Advertisements
Question
Prove the following result
`tan(cos^-1 4/5+tan^-1 2/3)=17/6`
Advertisements
Solution
LHS=`tan(cos^-1 4/5+tan^-1 2/3)=tan(tan^-1 sqrt(1-(4/5)^2)/(4/5)+tan^-1 2/3)` `[thereforecos^-1x=tan^-1(sqrt(1-x^2)/x)]`
`=tan(tan^-1 3/4+tan^-1 2/3)`
`=tan[tan^-1((3/4+2/3)/(1-3/4xx2/3))]` `[thereforetan^-1x+tan^-1y=tan^-1((x+y)/(1-xy))]`
`=tan[tan^-1((17/12)/(6/12))`
`=tan[tan^-1 17/6]`
`=17/6=`RHS
APPEARS IN
RELATED QUESTIONS
If `cos^-1( x/a) +cos^-1 (y/b)=alpha` , prove that `x^2/a^2-2(xy)/(ab) cos alpha +y^2/b^2=sin^2alpha`
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
Find the domain of `f(x)=cos^-1x+cosx.`
Find the principal values of the following:
`cos^-1(-1/sqrt2)`
Evaluate the following:
`sec^-1(sec pi/3)`
Evaluate the following:
`cot^-1{cot ((21pi)/4)}`
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{2tan^-1sqrt((1-x)/(1+x))}`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Evaluate:
`cot(tan^-1a+cot^-1a)`
`tan^-1x+2cot^-1x=(2x)/3`
Solve the following equation for x:
`tan^-1 2x+tan^-1 3x = npi+(3pi)/4`
Solve the following equation for x:
tan−1(x −1) + tan−1x tan−1(x + 1) = tan−13x
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
Evaluate the following:
`sin(2tan^-1 2/3)+cos(tan^-1sqrt3)`
`tan^-1 2/3=1/2tan^-1 12/5`
Prove that
`sin{tan^-1 (1-x^2)/(2x)+cos^-1 (1-x^2)/(2x)}=1`
Find the value of the following:
`tan^-1{2cos(2sin^-1 1/2)}`
Write the value of cos−1 (cos 1540°).
Write the value of sin−1 \[\left( \cos\frac{\pi}{9} \right)\]
Show that \[\sin^{- 1} (2x\sqrt{1 - x^2}) = 2 \sin^{- 1} x\]
Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Find the value of \[2 \sec^{- 1} 2 + \sin^{- 1} \left( \frac{1}{2} \right)\]
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
2 tan−1 {cosec (tan−1 x) − tan (cot−1 x)} is equal to
The number of solutions of the equation \[\tan^{- 1} 2x + \tan^{- 1} 3x = \frac{\pi}{4}\] is
\[\text{ If }\cos^{- 1} \frac{x}{3} + \cos^{- 1} \frac{y}{2} = \frac{\theta}{2}, \text{ then }4 x^2 - 12xy \cos\frac{\theta}{2} + 9 y^2 =\]
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] is equal to
\[\cot\left( \frac{\pi}{4} - 2 \cot^{- 1} 3 \right) =\]
If x > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to
If y = sin (sin x), prove that \[\frac{d^2 y}{d x^2} + \tan x \frac{dy}{dx} + y \cos^2 x = 0 .\]
Find the domain of `sec^(-1)(3x-1)`.
Find the domain of `sec^(-1) x-tan^(-1)x`
The period of the function f(x) = tan3x is ____________.
The value of tan `("cos"^-1 4/5 + "tan"^-1 2/3) =`
