Advertisements
Advertisements
Question
The value of `tan(cos^-1 3/5 + tan^-1 1/4)` is ______.
Options
`19/8`
`8/19`
`19/12`
`3/4`
Solution
The value of `tan(cos^-1 3/5 + tan^-1 1/4)` is `19/8`.
Explanation:
`tan(cos^-1 3/5 + tan^-1 1/4) = tan(tan^-1 4/3 + tan^-1 1/4)`
= `tan^-1 ((4/3 + 1/4)/(1 - 4/3 xx 1/4))`
= `tan^1 (19/8)`
= `19/8`.
APPEARS IN
RELATED QUESTIONS
Find the value of `tan^(-1) sqrt3 - cot^(-1) (-sqrt3)`
Solve `3tan^(-1)x + cot^(-1) x = pi`
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:
`sin^-1(cos (3pi)/4)`
Find the principal value of the following:
`sin^-1(tan (5pi)/4)`
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)`
Find the principal value of the following:
`tan^-1(cos pi/2)`
For the principal value, evaluate the following:
`sin^-1(-sqrt3/2)+\text{cosec}^-1(-2/sqrt3)`
Show that `"sin"^-1(5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`
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 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))`
The principal value branch of sec–1 is ______.
The value of `sin^-1 (cos((43pi)/5))` is ______.
The domain of sin–1 2x is ______.
The principal value of `sin^-1 ((-sqrt(3))/2)` is ______.
The greatest and least values of (sin–1x)2 + (cos–1x)2 are respectively ______.
The value of the expression sin [cot–1 (cos (tan–11))] is ______.
The value of sin (2 tan–1(0.75)) is equal to ______.
The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy 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`.
Which of the following is the principal value branch of `"cos"^-1 "x"`
What is the value of x so that the seven-digit number 8439 × 53 is divisible by 99?
