Advertisements
Advertisements
Question
If 3 tan–1x + cot–1x = π, then x equals ______.
Options
0
1
– 1
`1/2`
Solution
If 3 tan–1x + cot–1x = π, then x equals 1.
Explanation:
Given that 3 tan–1x + cot–1x = π
⇒ 2 tan–1x + tan–1x + cot–1x = π
⇒ `2 tan^-1x + pi/2` = π ......`[because tan^-1x + cot^-1x = pi/2]`
⇒ `2tan^-1x = pi - pi/2`
⇒ `2tan^-1x = pi/2`
⇒ `2tan^-1x = pi/4`
⇒ `tan^-1x = tan^-1(1)`
⇒ x = 1
APPEARS IN
RELATED QUESTIONS
Prove `2 tan^(-1) 1/2 + tan^(-1) 1/7 = tan^(-1) 31/17`
Find the value of `cot(tan^(-1) a + cot^(-1) a)`
Find the value of the given expression.
`tan^(-1) (tan (3pi)/4)`
Prove that:
`cos^(-1) 4/5 + cos^(-1) 12/13 = cos^(-1) 33/65`
Prove that:
`cos^(-1) 12/13 + sin^(-1) 3/5 = sin^(-1) 56/65`
Find: ∫ sin x · log cos x dx
Solve: tan-1 4 x + tan-1 6x `= π/(4)`.
Find the value, if it exists. If not, give the reason for non-existence
`tan^-1(sin(- (5pi)/2))`
Find the value of the expression in terms of x, with the help of a reference triangle
cos (tan–1 (3x – 1))
Find the value of `cot[sin^-1 3/5 + sin^-1 4/5]`
Choose the correct alternative:
sin–1(2 cos2x – 1) + cos–1(1 – 2 sin2x) =
Choose the correct alternative:
If `cot^-1(sqrt(sin alpha)) + tan^-1(sqrt(sin alpha))` = u, then cos 2u is equal to
If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is ______.
If α ≤ 2 sin–1x + cos–1x ≤ β, then ______.
If y = `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` for all x, then ______ < y < ______.
The minimum value of sinx - cosx is ____________.
Solve for x : `"sin"^-1 2 "x" + sin^-1 3"x" = pi/3`
If `"tan"^-1 ("cot" theta) = 2theta, "then" theta` is equal to ____________.
`"sin" {2 "cos"^-1 ((-3)/5)}` is equal to ____________.
The domain of the function defind by f(x) `= "sin"^-1 sqrt("x" - 1)` is ____________.
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
If `"tan"^-1 (("x" - 1)/("x" + 2)) + "tan"^-1 (("x" + 1)/("x" + 2)) = pi/4,` then x is equal to ____________.
`"cos"^-1["cos"(2"cot"^-1(sqrt2 - 1))]` = ____________.
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
`"cos"^-1 (1/2)`
The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. “A” is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby. Ram, Robert and Rahim suggested to the firm to place the hoarding board at three different locations namely C, D and E. “C” is at the height of 10 metres from the ground level. For viewer A, the angle of elevation of “D” is double the angle of elevation of “C” The angle of elevation of “E” is triple the angle of elevation of “C” for the same viewer. Look at the figure given and based on the above information answer the following:
Measure of ∠CAB = ________.
What is the simplest form of `tan^-1 sqrt(1 - x^2 - 1)/x, x ≠ 0`
If sin–1x + sin–1y + sin–1z = π, show that `x^2 - y^2 - z^2 + 2yzsqrt(1 - x^2) = 0`
