Advertisements
Advertisements
Question
`tan^-1 1/4+tan^-1 2/9=1/2cos^-1 3/2=1/2sin^-1(4/5)`
Advertisements
Solution
LHS = `tan^-1 1/4+tan^-1 2/9`
`=tan^-1((1/4+2/9)/(1-1/4xx2/9))` `[becausetan^-1x+tan^-1y=tan^-1((x+y)/(1-xy))]`
`=tan^-1((17/36)/(34/36))`
`=tan^-1 1/2`
`=1/2cos^-1((1-1/4)/(1+1/4))` `[becausetan^-1x=1/2cos^-1((1-x^2)/(1+x^2))]`
`=1/2cos^-1((3/4)/(5/4))`
`=1/2cos^-1(3/5)`
Now,
`tan^-1 1/2=1/2sin^-1((2/2)/(1+1/4))` `[becausetan^-1x=1/2sin^-1((2x)/(1+x^2))]`
`=1/2sin^-1 (1/(5/4))`
`=1/2sin^-1(4/5)`
APPEARS IN
RELATED QUESTIONS
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.`
`sin^-1(sin (5pi)/6)`
Evaluate the following:
`tan^-1(tan (6pi)/7)`
Evaluate the following:
`tan^-1(tan (7pi)/6)`
Evaluate the following:
`sec^-1(sec pi/3)`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`sec^-1(sec (7pi)/3)`
Evaluate the following:
`cot^-1(cot (9pi)/4)`
Evaluate the following:
`cot^-1{cot ((21pi)/4)}`
Write the following in the simplest form:
`sin^-1{(sqrt(1+x)+sqrt(1-x))/2},0<x<1`
Evaluate the following:
`sin(cos^-1 5/13)`
Evaluate:
`cot(tan^-1a+cot^-1a)`
Evaluate:
`cos(sec^-1x+\text(cosec)^-1x)`,|x|≥1
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
Solve the following equation for x:
`tan^-1((1-x)/(1+x))-1/2 tan^-1x` = 0, where x > 0
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
`(9pi)/8-9/4sin^-1 1/3=9/4sin^-1 (2sqrt2)/3`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
`2sin^-1 3/5-tan^-1 17/31=pi/4`
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=pi/2`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
Write the range of tan−1 x.
Write the value of cos−1 (cos 1540°).
Evaluate sin \[\left( \tan^{- 1} \frac{3}{4} \right)\]
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
If \[\sin^{- 1} \left( \frac{1}{3} \right) + \cos^{- 1} x = \frac{\pi}{2},\] then find x.
Write the value of \[\sin^{- 1} \left( \frac{1}{3} \right) - \cos^{- 1} \left( - \frac{1}{3} \right)\]
If 4 sin−1 x + cos−1 x = π, then what is the value of x?
The set of values of `\text(cosec)^-1(sqrt3/2)`
If \[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\] , find the value of x.
If \[\cos^{- 1} \frac{x}{a} + \cos^{- 1} \frac{y}{b} = \alpha, then\frac{x^2}{a^2} - \frac{2xy}{ab}\cos \alpha + \frac{y^2}{b^2} = \]
\[\text{ If }\cos^{- 1} \frac{x}{3} + \cos^{- 1} \frac{y}{2} = \frac{\theta}{2}, \text{ then }4 x^2 - 12xy \cos\frac{\theta}{2} + 9 y^2 =\]
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
\[\cot\left( \frac{\pi}{4} - 2 \cot^{- 1} 3 \right) =\]
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
The value of tan `("cos"^-1 4/5 + "tan"^-1 2/3) =`
