Advertisements
Advertisements
Question
The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is ______.
Advertisements
Solution
The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is – 1.
Explanation:
The given result is true when xy > – 1.
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(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)`
For the principal value, evaluate of the following:
`tan^-1(-1)+cos^-1(-1/sqrt2)`
For the principal value, evaluate of the following:
`tan^-1{2sin(4cos^-1 sqrt3/2)}`
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:
`\text(cosec)^-1(2/sqrt3)`
For the principal value, evaluate the following:
`sec^-1(sqrt2)+2\text{cosec}^-1(-sqrt2)`
Find the principal value of the following:
`cot^-1(-1/sqrt3)`
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)`.
Find the value of `tan^-1 (tan (9pi)/8)`.
Find the values of x which satisfy the equation sin–1x + sin–1(1 – x) = cos–1x.
One branch of cos–1 other than the principal value branch corresponds to ______.
The value of sin (2 sin–1 (.6)) is ______.
The value of `tan(cos^-1 3/5 + tan^-1 1/4)` 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)`
Find the value of the expression `sin(2tan^-1 1/3) + cos(tan^-1 2sqrt(2))`
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to ______.
The principal value of `cos^-1 (- 1/2)` is ______.
The value of `sin^-1 (sin (3pi)/5)` is ______.
The principal value of `tan^-1 sqrt(3)` is ______.
The least numerical value, either positive or negative of angle θ is called principal value of the inverse trigonometric function.
The minimum value of n for which `tan^-1 "n"/pi > pi/4`, n ∈ N, is valid is 5.
If `"tan"^-1 ("a"/"x") + "tan"^-1 ("b"/"x") = pi/2,` then x is equal to ____________.
Which of the following is the principal value branch of `"cos"^-1 "x"`
What is the principle value of `sin^-1 (1/sqrt(2))`?
Assertion (A): Maximum value of (cos–1 x)2 is π2.
Reason (R): Range of the principal value branch of cos–1 x is `[(-π)/2, π/2]`.
