Advertisements
Advertisements
प्रश्न
Find the principal value of the following:
`cosec^-1(-sqrt2)`
उत्तर
Let `cosec^-1(-sqrt2)=y`
Then,
`cosecy=-sqrt2`
We know that the range of the principal value branch is `[-pi/2,pi/2]-{0}`.
Thus,
`cosecy=-sqrt2=cosec(-pi/4)`
`y=-pi/4in [-pi/2,pi/2],y!=0`
Hence, the principal value of `cosec^-1(-sqrt2) is -pi/4.`
APPEARS IN
संबंधित प्रश्न
Write the principal value of `tan^(-1)+cos^(-1)(-1/2)`
The principal solution of the equation cot x=`-sqrt 3 ` is
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(-sqrt3/2)`
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:
`tan^-1(cos pi/2)`
Find the principal value of the following:
`sec^-1(-sqrt2)`
Find the principal value of the following:
cosec-1(-2)
For the principal value, evaluate the following:
`sec^-1(sqrt2)+2\text{cosec}^-1(-sqrt2)`
Find the principal value of the following:
`cot^-1(-1/sqrt3)`
Show that `"sin"^-1(5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`
Solve for x, if:
tan (cos-1x) = `2/sqrt5`
If `sin^-1"x" + tan^-1"x" = pi/2`, prove that `2"x"^2 + 1 = sqrt5`
Find the value of `cos^-1(cos (13pi)/6)`.
Find the value of `tan^-1 (tan (9pi)/8)`.
Find value of tan (cos–1x) and hence evaluate `tan(cos^-1 8/17)`
Find the value of `sin[2cot^-1 ((-5)/12)]`
Find the value of `sin(2tan^-1 2/3) + cos(tan^-1 sqrt(3))`
Which of the following corresponds to the principal value branch of tan–1?
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 value of cot (sin–1x) 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 ______.
Find the value of `tan^-1 (tan (5pi)/6) +cos^-1(cos (13pi)/6)`
Which of the following is the principal value branch of cos–1x?
The value of sin (2 tan–1(0.75)) is equal to ______.
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 the expression (cos–1x)2 is equal to sec2x.
The general solution of the equation `"cot" theta - "tan" theta = "sec" theta` is ____________ where `(n in I).`
`2 "cos"^-1 "x = sin"^-1 (2"x" sqrt(1 - "x"^2))` is true for ____________.
Assertion (A): Maximum value of (cos–1 x)2 is π2.
Reason (R): Range of the principal value branch of cos–1 x is `[(-π)/2, π/2]`.
