Advertisements
Advertisements
Question
The value of sin (2 tan–1(0.75)) is equal to ______.
Options
0.75
1.5
0.96
sin 1.5
Advertisements
Solution
The value of sin (2 tan–1(0.75)) is equal to 0.96.
Explanation:
We have, sin [2 tan–1(0.75))]
= `sin(2 tan^-1 3/4)`
= `sin(sin^-1 (2* 3/4)/(1 + 9/16))` ......`(because 2 tan^-1x = sin^-1 (2x)/(1 + x^2))`
= `sin(sin^-1 (3/2)/(25/16))`
= `sin(sin^-1 24/25)`
= `24/25`
= 0.96
APPEARS IN
RELATED QUESTIONS
The principal solution of `cos^-1(-1/2)` is :
Write the principal value of `tan^(-1)+cos^(-1)(-1/2)`
Find the principal value of the following:
`sin^-1(-sqrt3/2)`
Find the principal value of the following:
`sin^-1(cos (2pi)/3)`
Find the principal value of the following:
`sin^-1(cos (3pi)/4)`
Find the principal value of the following:
`sin^-1(tan (5pi)/4)`
Find the principal value of the following:
`sec^-1(2)`
For the principal value, evaluate the following:
`tan^-1sqrt3-sec^-1(-2)`
For the principal value, evaluate the following:
`sec^-1(sqrt2)+2\text{cosec}^-1(-sqrt2)`
For the principal value, evaluate the following:
`sin^-1[cos{2\text(cosec)^-1(-2)}]`
For the principal value, evaluate the following:
`cosec^-1(2tan (11pi)/6)`
Show that `"sin"^-1(5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`
Show that `"sin"^-1(5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`
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`
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)`.
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 `sec(tan^-1 y/2)`
Find value of tan (cos–1x) and hence evaluate `tan(cos^-1 8/17)`
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 value of `sin^-1 (cos((43pi)/5))` is ______.
The value of cot (sin–1x) is ______.
The value of tan2 (sec–12) + cot2 (cosec–13) is ______.
Find the value of `tan^-1 (tan (5pi)/6) +cos^-1(cos (13pi)/6)`
Find the value of `tan^-1 (tan (2pi)/3)`
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 ______.
The principal value of `cos^-1 (- 1/2)` is ______.
The value of `sin^-1 (sin (3pi)/5)` is ______.
The principal value of `sin^-1 [cos(sin^-1 1/2)]` is `pi/3`.
What is the value of `tan^-1(1) cos^-1(- 1/2) + sin^-1(- 1/2)`
