Advertisements
Advertisements
प्रश्न
For the principal value, evaluate of the following:
`sin^-1(-sqrt3/2)+cos^-1(sqrt3/2)`
उत्तर
`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
संबंधित प्रश्न
For the principal value, evaluate of the following:
`cos^-1 1/2+2sin^-1 (1/2)`
For the principal value, evaluate of the following:
`sin^-1(-1/2)+2cos^-1(-sqrt3/2)`
Find the principal value of the following:
`tan^-1(cos pi/2)`
Find the principal value of the following:
`sec^-1(2)`
Find the principal value of the following:
`sec^-1(2sin (3pi)/4)`
For the principal value, evaluate the following:
`sin^-1(-sqrt3/2)-2sec^-1(2tan pi/6)`
For the principal value, evaluate the following:
`cosec^-1(2tan (11pi)/6)`
Find the principal value of the following:
`cot^-1(-1/sqrt3)`
if sec-1 x = cosec-1 v. show that `1/x^2 + 1/y^2 = 1`
Solve for x, if:
tan (cos-1x) = `2/sqrt5`
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 |
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))`
The value of `sin^-1 (cos((43pi)/5))` is ______.
The principal value of the expression cos–1[cos (– 680°)] is ______.
The domain of sin–1 2x is ______.
The value of sin (2 sin–1 (.6)) is ______.
The value of the expression sin [cot–1 (cos (tan–11))] is ______.
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to ______.
The value of sin (2 tan–1(0.75)) is equal to ______.
The value of `cos^-1 (cos (3pi)/2)` is equal to ______.
If `cos(tan^-1x + cot^-1 sqrt(3))` = 0, then value of x is ______.
The value of cos (sin–1x + cos–1x), |x| ≤ 1 is ______.
The value of expression `tan((sin^-1x + cos^-1x)/2)`, when x = `sqrt(3)/2` is ______.
The value of the expression (cos–1x)2 is equal to sec2x.
The minimum value of n for which `tan^-1 "n"/pi > pi/4`, n ∈ N, is valid is 5.
The period of the function f(x) = cos4x + tan3x is ____________.
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 ____________.
If `"tan"^-1 ("a"/"x") + "tan"^-1 ("b"/"x") = pi/2,` then 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 ____________.
What is the principal value of `cot^-1 ((-1)/sqrt(3))`?
