Advertisements
Advertisements
प्रश्न
Find the value of `sin(2tan^-1 2/3) + cos(tan^-1 sqrt(3))`
उत्तर
Let `tan-1 2/3` = x and `tan^-1 sqrt(3)` = y
So that tan x = `2/3` and tan y = `sqrt(3)`
Therefore, `sin(2tan^-1 2/3) + cos(tan^-1 sqrt(3))`
= sin (2x) + cos y
= `(2tanx)/(1 + tan^2x)+/sqrt(1 +tan^2y)`
= `(2*2/3)/(1 + 4/9) + 1/( + sqrt((sqrt(3))^2`
= `12/13 +1/2`
= `37/26`.
APPEARS IN
संबंधित प्रश्न
Write the principal value of `tan^(-1)+cos^(-1)(-1/2)`
Solve `3tan^(-1)x + cot^(-1) x = pi`
Find the principal value of the following:
`sin^-1(cos (2pi)/3)`
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(1/sqrt3)`
For the principal value, evaluate the following:
`tan^-1sqrt3-sec^-1(-2)`
For the principal value, evaluate the following:
`sin^-1(-sqrt3/2)-2sec^-1(2tan pi/6)`
Find the principal value of the following:
`cosec^-1(-sqrt2)`
For the principal value, evaluate the following:
`sin^-1[cos{2\text(cosec)^-1(-2)}]`
Find the principal value of the following:
`cot^-1(sqrt3)`
if sec-1 x = cosec-1 v. show that `1/x^2 + 1/y^2 = 1`
If `sin^-1"x" + tan^-1"x" = pi/2`, prove that `2"x"^2 + 1 = 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 `cos^-1(cos (13pi)/6)`.
Which of the following corresponds to the principal value branch of tan–1?
The domain of sin–1 2x is ______.
The principal value of `sin^-1 ((-sqrt(3))/2)` is ______.
Find the value of `tan^-1 (- 1/sqrt(3)) + cot^-1(1/sqrt(3)) + tan^-1(sin((-pi)/2))`
Find the value of `tan^-1 (tan (2pi)/3)`
The value of `sin^-1 [cos((33pi)/5)]` is ______.
The domain of the function cos–1(2x – 1) is ______.
The domain of the function defined by f(x) = `sin^-1 sqrt(x- 1)` is ______.
The value of `cot[cos^-1 (7/25)]` 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`.
If `"tan"^-1 "x" + "tan"^-1"y + tan"^-1 "z" = pi/2, "x,y,x" > 0,` then the value of xy+yz+zx is ____________.
