Advertisements
Advertisements
Question
Find the value of `4tan^-1 1/5 - tan^-1 1/239`
Advertisements
Solution
`4tan^-1 1/5 - tan^-1 1/239`
= `2(2tan^-1 1/5) - tan^-1 1/239`
= `2tan^-1 (2/5)/(1 - (1/5)^2) - tan^-1 1/239` .....`(because 2tan^-1x = tan^-1 (2x)/(1 - x^2))`
= `2tan^-1 (2/5)/(24/25) - tan^-1 1/239`
= `2tan^-1 5/12 - tan^-1 1/239`
= `2tan^-1 (2/5)/(1 - (1/5)^2) - tan^-1 1/239` .....`(because 2tan^-1x = tan^-1 (2x)/(1 - x^2))`
= `2tan^-1 (2/5)/(24/25) - tan^-1 1/239`
= `2tan^-1 5/12 - tan^-1 1/239`
= `tan^-1 (2*5/12)/(1 - (5/12)^2) - tan^-1 1/239` ......`(because 2tan^-1x = tan^-1 (2x)/(1 - x^2))`
= `tan^-1 (144 xx 5)/(119 xx 6) - tan^-1 1/239`
= `tan^-1 120/119 - tan^-1 1/239`
= `tan^-1 (120/119 - 1/239)/(1 + 120/119 * 1/239)` ......`(because tan^-1x - tan^-1y = tan^-1 (x - y)/(1 + xy))`
= `tan^-1 (120 xx 239 - 119)/(119 xx 239 + 120)`
= `tan^-1 (28680 - 119)/(28441 + 120)`
= `tan^-1 28561/28561`
= `tan^-1 1 = pi/4`
APPEARS IN
RELATED QUESTIONS
The principal solution of the equation cot x=`-sqrt 3 ` is
Find the value of `tan^(-1) sqrt3 - cot^(-1) (-sqrt3)`
Solve `3tan^(-1)x + cot^(-1) x = pi`
if `tan^(-1) a + tan^(-1) b + tan^(-1) x = pi`, prove that a + b + c = abc
Find the principal value of the following:
`sin^-1(cos (2pi)/3)`
Find the principal value of the following:
`sin^-1((sqrt3-1)/(2sqrt2))`
Find the principal value of the following:
`sin^-1((sqrt3+1)/(2sqrt2))`
Find the principal value of the following:
`sin^-1(tan (5pi)/4)`
For the principal value, evaluate of the following:
`sin^-1(-1/2)+2cos^-1(-sqrt3/2)`
For the principal value, evaluate the following:
`tan^-1sqrt3-sec^-1(-2)`
Find the principal value of the following:
`\text(cosec)^-1(2/sqrt3)`
For the principal value, evaluate the following:
`sin^-1(-sqrt3/2)+\text{cosec}^-1(-2/sqrt3)`
For the principal value, evaluate the following:
`sec^-1(sqrt2)+2\text{cosec}^-1(-sqrt2)`
For the principal value, evaluate the following:
`sin^-1[cos{2\text(cosec)^-1(-2)}]`
if sec-1 x = cosec-1 v. show that `1/x^2 + 1/y^2 = 1`
Find the principal value of cos–1x, for x = `sqrt(3)/2`.
Prove that tan(cot–1x) = cot(tan–1x). State with reason whether the equality is valid for all values of x.
Find value of tan (cos–1x) and hence evaluate `tan(cos^-1 8/17)`
The principal value branch of sec–1 is ______.
The domain of sin–1 2x is ______.
The greatest and least values of (sin–1x)2 + (cos–1x)2 are respectively ______.
Let θ = sin–1 (sin (– 600°), then value of θ is ______.
The value of the expression sin [cot–1 (cos (tan–11))] is ______.
Find the value of `tan^-1 (tan (2pi)/3)`
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to ______.
The value of the expression `2 sec^-1 2 + sin^-1 (1/2)` is ______.
The value of `cot[cos^-1 (7/25)]` is ______.
The principal value of `cos^-1 (- 1/2)` is ______.
If `cos(tan^-1x + cot^-1 sqrt(3))` = 0, then value of x is ______.
The value of expression `tan((sin^-1x + cos^-1x)/2)`, when x = `sqrt(3)/2` is ______.
The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is ______.
The principal value of `sin^-1 [cos(sin^-1 1/2)]` is `pi/3`.
If `5 sin theta = 3 "then", (sec theta + tan theta)/(sec theta - tan theta)` is equal to ____________.
The period of the function f(x) = cos4x + tan3x is ____________.
`2 "cos"^-1 "x = sin"^-1 (2"x" sqrt(1 - "x"^2))` is true for ____________.
If sin `("sin"^-1 1/5 + "cos"^-1 "x") = 1,` then the value of x is ____________.
`"sec" {"tan"^-1 (-"y"/3)}` is equal to ____________.
