Advertisements
Advertisements
Question
Evaluate tan (tan–1(– 4)).
Advertisements
Solution
Since tan (tan–1x) = x, ∀ x ∈ R, tan (tan–1(– 4)
= – 4.
APPEARS IN
RELATED QUESTIONS
If `sin (sin^(−1)(1/5)+cos^(−1) x)=1`, then find the value of x.
Prove the following:
3 sin−1 x = sin−1 (3x − 4x3), `x ∈ [-1/2, 1/2]`
Write the function in the simplest form: `tan^(-1) ((cos x - sin x)/(cos x + sin x)) `,` 0 < x < pi`
Write the following function in the simplest form:
`tan^(-1) x/(sqrt(a^2 - x^2))`, |x| < a
Find the value of the following:
`tan^-1 [2 cos (2 sin^-1 1/2)]`
Prove that:
`cos^(-1) 12/13 + sin^(-1) 3/5 = sin^(-1) 56/65`
Prove `tan^(-1) 1/5 + tan^(-1) (1/7) + tan^(-1) 1/3 + tan^(-1) 1/8 = pi/4`
Prove `(9pi)/8 - 9/4 sin^(-1) 1/3 = 9/4 sin^(-1) (2sqrt2)/3`
Prove that `3sin^(-1)x = sin^(-1) (3x - 4x^3)`, `x in [-1/2, 1/2]`
If y = `(x sin^-1 x)/sqrt(1 -x^2)`, prove that: `(1 - x^2)dy/dx = x + y/x`
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 (cos pi)`
If tan–1x + tan–1y + tan–1z = π, show that x + y + z = xyz
Simplify: `tan^-1 x/y - tan^-1 (x - y)/(x + y)`
Choose the correct alternative:
sin(tan–1x), |x| < 1 is equal to
Evaluate: `tan^-1 sqrt(3) - sec^-1(-2)`.
Prove that `2sin^-1 3/5 - tan^-1 17/31 = pi/4`
Solve the equation `sin^-1 6x + sin^-1 6sqrt(3)x = - pi/2`
If `sin^-1 ((2"a")/(1 + "a"^2)) + cos^-1 ((1 - "a"^2)/(1 + "a"^2)) = tan^-1 ((2x)/(1 - x^2))`. where a, x ∈ ] 0, 1, then the value of x is ______.
If y = `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` for all x, then ______ < y < ______.
The value of cot–1(–x) for all x ∈ R in terms of cot–1x is ______.
The maximum value of sinx + cosx is ____________.
Solve for x : `"sin"^-1 2 "x" + sin^-1 3"x" = pi/3`
If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt"cos" alpha) = "x",` the sinx is equal to ____________.
The value of cot `("cosec"^-1 5/3 + "tan"^-1 2/3)` is ____________.
The value of expression 2 `"sec"^-1 2 + "sin"^-1 (1/2)`
The value of the expression tan `(1/2 "cos"^-1 2/sqrt3)`
If tan-1 2x + tan-1 3x = `pi/4,` then x is ____________.
The value of cot-1 9 + cosec-1 `(sqrt41/4)` is given by ____________.
The value of `"tan"^-1 (1/2) + "tan"^-1(1/3) + "tan"^-1(7/8)` is ____________.
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
The value of `"cos"^-1 ("cos" ((33pi)/5))` is ____________.
If `6"sin"^-1 ("x"^2 - 6"x" + 8.5) = pi,` then x is equal to ____________.
If `"sin"^-1 (1 - "x") - 2 "sin"^-1 ("x") = pi/2,` then x is equal to ____________.
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:

𝐴' Is another viewer standing on the same line of observation across the road. If the width of the road is 5 meters, then the difference between ∠CAB and ∠CA'B is ______.
What is the simplest form of `tan^-1 sqrt(1 - x^2 - 1)/x, x ≠ 0`
If `cos^-1(2/(3x)) + cos^-1(3/(4x)) = π/2(x > 3/4)`, then x is equal to ______.
Write the following function in the simplest form:
`tan^-1 ((cos x - sin x)/(cos x + sin x)), (-pi)/4 < x < (3 pi)/4`
