Advertisements
Advertisements
Question
For the principal value, evaluate of the following:
`sin^-1(-sqrt3/2)+cos^-1(sqrt3/2)`
Solution
`sin^-1(-sqrt3/2)+cos^-1(sqrt3/2)`
`=sin^-1{sin(-pi/2)}+cos^-1(cos pi/6)`
`=-pi/3+pi/6` `[because"Range of sine is"[-pi/2,pi/2]; -pi/3 in [-pi/2, pi/2] "and range of cosine is" [0,pi] ; pi/6 in [0, pi]]`
`=-pi/6`
`therefore sin^-1(-sqrt3/2)+cos^-1(sqrt3/2)=-pi/6`
APPEARS IN
RELATED QUESTIONS
Find the value of `tan^(-1) sqrt3 - cot^(-1) (-sqrt3)`
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((sqrt3-1)/(2sqrt2))`
For the principal value, evaluate of the following:
`cos^-1 1/2+2sin^-1 (1/2)`
Find the principal value of the following:
`tan^-1(cos pi/2)`
Find the principal value of the following:
`sec^-1(2tan (3pi)/4)`
Find the principal value of the following:
`cosec^-1(2cos (2pi)/3)`
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)`
Find the principal value of the following:
`cot^-1(-sqrt3)`
Find the principal value of the following:
`cot^-1(-1/sqrt3)`
The index number by the method of aggregates for the year 2010, taking 2000 as the base year, was found to be 116. If sum of the prices in the year 2000 is ₹ 300, find the values of x and y in the data given below
| Commodity | A | B | C | D | E | F |
| Price in the year 2000 (₹) | 50 | x | 30 | 70 | 116 | 20 |
| Price in the year 2010 (₹) | 60 | 24 | y | 80 | 120 | 28 |
Find the principal value of cos–1x, for x = `sqrt(3)/2`.
Find the value of `tan^-1 (tan (9pi)/8)`.
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 of `sin^-1 ((-sqrt(3))/2)` is ______.
Let θ = sin–1 (sin (– 600°), then value of θ is ______.
The value of `tan(cos^-1 3/5 + tan^-1 1/4)` is ______.
Which of the following is the principal value branch of cosec–1x?
The value of `sin^-1 [cos((33pi)/5)]` is ______.
The domain of the function cos–1(2x – 1) is ______.
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to ______.
The value of `cos^-1 (cos (3pi)/2)` is equal to ______.
The value of `cot[cos^-1 (7/25)]` is ______.
The value of `sin^-1 (sin (3pi)/5)` is ______.
The principal value of `tan^-1 sqrt(3)` is ______.
The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is ______.
The least numerical value, either positive or negative of angle θ is called principal value of the inverse trigonometric function.
The principal value of `sin^-1 [cos(sin^-1 1/2)]` is `pi/3`.
The period of the function f(x) = cos4x + tan3x is ____________.
What is the value of x so that the seven-digit number 8439 × 53 is divisible by 99?
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]`.
Evaluate `sin^-1 (sin (3π)/4) + cos^-1 (cos π) + tan^-1 (1)`.
