Advertisements
Advertisements
Question
Find the value of `tan^(-1) sqrt3 - cot^(-1) (-sqrt3)`
Solution
`tan^(-1) (sqrt3) -cot^(-1) (-sqrt3)`
`= tan^(-1) {tan (pi/3)} - cot^(-1) (cot (5pi)/6)` [∵ Range of `tan^(-1) is (-pi/2, pi/2); pi/3 in (-pi/2, pi/2)`
and range of `cot^(-1) is [0, pi]; (5pi)/6 in [0,pi]]`
`= pi/3 - (5pi)/6`
`= -pi/2`
APPEARS IN
RELATED QUESTIONS
The principal solution of the equation cot x=`-sqrt 3 ` is
Prove that `sin^(-1) (3/5) + cos^(-1) (12/13) = sin^(-1) (56/65)`
Solve `3tan^(-1)x + cot^(-1) x = pi`
Find the principal value of the following:
`sin^-1((sqrt3+1)/(2sqrt2))`
For the principal value, evaluate of the following:
`sin^-1(-sqrt3/2)+cos^-1(sqrt3/2)`
Find the principal value of the following:
`sec^-1(-sqrt2)`
For the principal value, evaluate the following:
`tan^-1sqrt3-sec^-1(-2)`
Find the principal value of the following:
`\text(cosec)^-1(2/sqrt3)`
Find the principal value of the following:
`cot^-1(tan (3pi)/4)`
Prove that tan(cot–1x) = cot(tan–1x). State with reason whether the equality is valid for all values of x.
Find the value of `sin(2tan^-1 2/3) + cos(tan^-1 sqrt(3))`
Find the values of x which satisfy the equation sin–1x + sin–1(1 – x) = cos–1x.
The principal value branch of sec–1 is ______.
One branch of cos–1 other than the principal value branch corresponds to ______.
The greatest and least values of (sin–1x)2 + (cos–1x)2 are respectively ______.
If sin–1x + sin–1y = `pi/2`, then value of cos–1x + cos–1y is ______.
The value of `tan(cos^-1 3/5 + tan^-1 1/4)` is ______.
The value of tan2 (sec–12) + cot2 (cosec–13) is ______.
Which of the following is the principal value branch of cos–1x?
The value of `sin^-1 [cos((33pi)/5)]` is ______.
The value of sin (2 tan–1(0.75)) is equal to ______.
The value of `cot[cos^-1 (7/25)]` is ______.
The principal value of `cos^-1 (- 1/2)` is ______.
The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is ______.
The value of the expression (cos–1x)2 is equal to sec2x.
The principal value of `sin^-1 [cos(sin^-1 1/2)]` is `pi/3`.
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 ____________.
`"cos" ["tan"^-1 {"sin" ("cot"^-1 "x")}]` is equal to ____________.
