Advertisements
Advertisements
Question
Prove the following result:
`tan^-1 1/4+tan^-1 2/9=sin^-1 1/sqrt5`
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`
`=sin^-1 (1/2)/sqrt(1+(1/2)^2)`
`=sin^-1 1/5=`RHS
APPEARS IN
RELATED QUESTIONS
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
`sin^-1(sin (13pi)/7)`
`sin^-1(sin (17pi)/8)`
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Evaluate the following:
`cos^-1(cos3)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`tan^-1(tan4)`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Evaluate the following:
`sec(sin^-1 12/13)`
Solve: `cos(sin^-1x)=1/6`
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
`5tan^-1x+3cot^-1x=2x`
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
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`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
Solve `cos^-1sqrt3x+cos^-1x=pi/2`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
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)}`
Find the value of the following:
`cos(sec^-1x+\text(cosec)^-1x),` | x | ≥ 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 sin−1
\[\left( \sin( -{600}°) \right)\].
Write the value of cos2 \[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]
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 \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the value of \[\sec^{- 1} \left( \frac{1}{2} \right)\]
2 tan−1 {cosec (tan−1 x) − tan (cot−1 x)} is equal to
The positive integral solution of the equation
\[\tan^{- 1} x + \cos^{- 1} \frac{y}{\sqrt{1 + y^2}} = \sin^{- 1} \frac{3}{\sqrt{10}}\text{ is }\]
If α = \[\tan^{- 1} \left( \tan\frac{5\pi}{4} \right) \text{ and }\beta = \tan^{- 1} \left( - \tan\frac{2\pi}{3} \right)\] , then
In a ∆ ABC, if C is a right angle, then
\[\tan^{- 1} \left( \frac{a}{b + c} \right) + \tan^{- 1} \left( \frac{b}{c + a} \right) =\]
Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
Find the value of `sin^-1(cos((33π)/5))`.
