Advertisements
Advertisements
Question
Find the principal value of the following:
`tan^-1(cos pi/2)`
Advertisements
Solution
Let `tan^-1(cos pi/2)=y`
Then,
`tany=cospi/2`
We know that the range of the principal value branch is `(-pi/2,pi/2)`
Thus,
`tany=cos pi/2=0=tan(0)`
`=>y=0in(-pi/2,pi/2)`
Hence, the principal value of `tan^-1(cos pi/2)` is 0.
APPEARS IN
RELATED QUESTIONS
Solve `3tan^(-1)x + cot^(-1) x = pi`
Find the principal value of the following:
`sin^-1(-sqrt3/2)`
Find the principal value of the following:
`sin^-1(cos (2pi)/3)`
Find the principal value of the following:
`sin^-1(tan (5pi)/4)`
For the principal value, evaluate of the following:
`sin^-1(-sqrt3/2)+cos^-1(sqrt3/2)`
Find the principal value of the following:
`tan^-1(1/sqrt3)`
Find the principal value of the following:
`tan^-1(-1/sqrt3)`
Find the principal value of the following:
`tan^-1(2cos (2pi)/3)`
For the principal value, evaluate of the following:
`tan^-1(-1)+cos^-1(-1/sqrt2)`
Find the principal value of the following:
`sec^-1(2tan (3pi)/4)`
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)`
Find the principal value of the following:
`cot^-1(-sqrt3)`
if sec-1 x = cosec-1 v. show that `1/x^2 + 1/y^2 = 1`
If `sin^-1"x" + tan^-1"x" = pi/2`, prove that `2"x"^2 + 1 = sqrt5`
Find the value of `sec(tan^-1 y/2)`
Find the values of x which satisfy the equation sin–1x + sin–1(1 – x) = cos–1x.
One branch of cos–1 other than the principal value branch corresponds to ______.
The principal value of the expression cos–1[cos (– 680°)] is ______.
The principal value of `sin^-1 ((-sqrt(3))/2)` is ______.
The greatest and least values of (sin–1x)2 + (cos–1x)2 are respectively ______.
The value of sin (2 sin–1 (.6)) is ______.
The value of `tan(cos^-1 3/5 + tan^-1 1/4)` is ______.
Find the value of `tan^-1 (- 1/sqrt(3)) + cot^-1(1/sqrt(3)) + tan^-1(sin((-pi)/2))`
The domain of the function cos–1(2x – 1) is ______.
The domain of the function defined by f(x) = `sin^-1 sqrt(x- 1)` is ______.
The value of `cot[cos^-1 (7/25)]` 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`.
`"cos" ["tan"^-1 {"sin" ("cot"^-1 "x")}]` is equal to ____________.
If `"tan"^-1 "x" + "tan"^-1"y + tan"^-1 "z" = pi/2, "x,y,x" > 0,` then the value of xy+yz+zx is ____________.
Which of the following is the principal value branch of `"cos"^-1 "x"`
What is the principal value of `cot^-1 ((-1)/sqrt(3))`?
