Advertisements
Advertisements
प्रश्न
The principal solution of `cos^-1(-1/2)` is :
पर्याय
`pi/3`
`pi/6`
`(2pi)/3`
`(3pi)/2`
उत्तर
The principal solution of `cos^-1(-1/2)= ` An angle in [0,π], whose cosine is -1/2
⇒ `cos^-1(-1/2) = pi - "cos"^-1 (1/2)` .....[because cos-1 (-x) = π - cos x]
`= pi - pi/3 = (2pi)/3`
APPEARS IN
संबंधित प्रश्न
The principal solution of the equation cot x=`-sqrt 3 ` is
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(cos (2pi)/3)`
Find the principal value of the following:
`sin^-1((sqrt3+1)/(2sqrt2))`
Find the principal value of the following:
`tan^-1(-1/sqrt3)`
For the principal value, evaluate of the following:
`tan^-1{2sin(4cos^-1 sqrt3/2)}`
Find the principal value of the following:
`sec^-1(2)`
Find the principal value of the following:
`sec^-1(2sin (3pi)/4)`
Find the principal value of the following:
`cosec^-1(-sqrt2)`
Find the principal value of the following:
`\text(cosec)^-1(2/sqrt3)`
Find the principal value of the following:
`cot^-1(sqrt3)`
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 |
Find the principal value of cos–1x, for x = `sqrt(3)/2`.
Find the value of `cos^-1(cos (13pi)/6)`.
Find the value of `sin[2cot^-1 ((-5)/12)]`
The principal value branch of sec–1 is ______.
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 value of the expression sin [cot–1 (cos (tan–11))] is ______.
Find the value of `tan^-1 (- 1/sqrt(3)) + cot^-1(1/sqrt(3)) + tan^-1(sin((-pi)/2))`
Which of the following is the principal value branch of cos–1x?
The value of `sin^-1 [cos((33pi)/5)]` is ______.
The domain of the function cos–1(2x – 1) is ______.
The value of sin (2 tan–1(0.75)) is equal to ______.
The value of the expression `2 sec^-1 2 + sin^-1 (1/2)` is ______.
The value of `cos^-1 (cos (14pi)/3)` is ______.
The value of expression `tan((sin^-1x + cos^-1x)/2)`, when x = `sqrt(3)/2` is ______.
The least numerical value, either positive or negative of angle θ is called principal value of the inverse trigonometric function.
`"cos" ["tan"^-1 {"sin" ("cot"^-1 "x")}]` is equal to ____________.
`"sec" {"tan"^-1 (-"y"/3)}` 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 value of `tan^-1(1) cos^-1(- 1/2) + sin^-1(- 1/2)`