Advertisements
Advertisements
प्रश्न
For the principal value, evaluate of the following:
`cos^-1 1/2 + 2 sin^-1 (1/2)`
Evaluate: `cos^-1 (1/2) + 2 sin^-1 (1/2)`
Advertisements
उत्तर
cos–1 (cos x) = x
sin–1 (sin x) = x
`cos^-1 1/2 + 2sin^-1 (1/2)`
= `cos^-1 (cos π/3) + 2 sin^-1 (sin π/6)`
= `π/3 + 2(π/6)`
= `(2π)/3`
संबंधित प्रश्न
The principal solution of `cos^-1(-1/2)` is :
Prove that `sin^(-1) (3/5) + cos^(-1) (12/13) = sin^(-1) (56/65)`
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((sqrt3-1)/(2sqrt2))`
Find the principal value of the following:
`sin^-1(cos (3pi)/4)`
Find the principal value of the following:
`sec^-1(-sqrt2)`
For the principal value, evaluate the following:
`tan^-1sqrt3-sec^-1(-2)`
Find the principal value of the following:
`cot^-1(-1/sqrt3)`
Find the principal value of the following:
`cot^-1(tan (3pi)/4)`
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 value of `sec(tan^-1 y/2)`
Find value of tan (cos–1x) and hence evaluate `tan(cos^-1 8/17)`
Find the values of x which satisfy the equation sin–1x + sin–1(1 – x) = cos–1x.
The value of cot (sin–1x) is ______.
The domain of sin–1 2x is ______.
Let θ = sin–1 (sin (– 600°), then value of θ is ______.
The value of sin (2 sin–1 (.6)) is ______.
If sin–1x + sin–1y = `pi/2`, then value of cos–1x + cos–1y is ______.
The value of `tan(cos^-1 3/5 + tan^-1 1/4)` is ______.
The value of tan2 (sec–12) + cot2 (cosec–13) is ______.
Which of the following is the principal value branch of cos–1x?
The domain of the function cos–1(2x – 1) is ______.
The value of sin (2 tan–1(0.75)) is equal to ______.
If tan–1x + tan–1y = `(4pi)/5`, then cot–1x + cot–1y equals ______.
The value of `sin^-1 (sin (3pi)/5)` is ______.
If `cos(tan^-1x + cot^-1 sqrt(3))` = 0, then value of x is ______.
The set of values of `sec^-1 (1/2)` is ______.
The value of expression `tan((sin^-1x + cos^-1x)/2)`, when x = `sqrt(3)/2` is ______.
The domain of trigonometric functions can be restricted to any one of their branch (not necessarily principal value) in order to obtain their inverse functions.
The principal value of `sin^-1 [cos(sin^-1 1/2)]` is `pi/3`.
`2 "cos"^-1 "x = sin"^-1 (2"x" sqrt(1 - "x"^2))` is true for ____________.
`"cos" ["tan"^-1 {"sin" ("cot"^-1 "x")}]` is equal to ____________.
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 ____________.
Which of the following is the principal value branch of `"cos"^-1 "x"`
