Advertisements
Advertisements
प्रश्न
Write the following function in the simplest form:
`tan^(-1) x/(sqrt(a^2 - x^2)), |x| < a`
Advertisements
उत्तर
`tan^(-1) x/(sqrt(a^2 - x^2))`
Put x = a sin θ
⇒ `x/a = sin θ`
⇒ `θ = sin^(-1) (x/a)`
∴ `tan^(-1) x/sqrt(a^2 - x^2) `
= `tan^(-1) ((a sin θ)/(sqrt(a^2 - a^2 sin^2 θ)))`
= `tan^(-1) ((asin θ)/(asqrt(1-sin^2 θ))) `
= `tan^(-1) ((asin θ)/(acos θ))`
= `tan^(-1) (tan θ)`
= θ
= `sin^(-1) x/a`
APPEARS IN
संबंधित प्रश्न
Prove that `cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2;x in (0,pi/4) `
Prove that: `tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4`
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 that `tan^(-1) 63/16 = sin^(-1) 5/13 + cos^(-1) 3/5`.
sin (tan–1 x), |x| < 1 is equal to ______.
sin–1 (1 – x) – 2 sin–1 x = `pi/2`, then x is equal to ______.
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 (cos pi)`
Find the value, if it exists. If not, give the reason for non-existence
`tan^-1(sin(- (5pi)/2))`
Find the value of `tan(sin^-1 3/5 + cot^-1 3/2)`
Prove that `tan^-1 2/11 + tan^-1 7/24 = tan^-1 1/2`
Choose the correct alternative:
The equation tan–1x – cot–1x = `tan^-1 (1/sqrt(3))` has
Evaluate `tan^-1(sin((-pi)/2))`.
Prove that `2sin^-1 3/5 - tan^-1 17/31 = pi/4`
Prove that cot–17 + cot–18 + cot–118 = cot–13
Show that `2tan^-1 {tan alpha/2 * tan(pi/4 - beta/2)} = tan^-1 (sin alpha cos beta)/(cosalpha + sinbeta)`
If α ≤ 2 sin–1x + cos–1x ≤ β, then ______.
Evaluate `cos[cos^-1 ((-sqrt(3))/2) + pi/6]`
Prove that `tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/((1 + x^2) - sqrt(1 - x^2))) = pi/2 + 1/2 cos^-1x^2`
If 3 tan–1x + cot–1x = π, then x equals ______.
The maximum value of sinx + cosx is ____________.
If `"tan"^-1 ("cot" theta) = 2theta, "then" theta` is equal to ____________.
The value of cot `("cosec"^-1 5/3 + "tan"^-1 2/3)` is ____________.
The value of the expression tan `(1/2 "cos"^-1 2/sqrt3)`
If x = a sec θ, y = b tan θ, then `("d"^2"y")/("dx"^2)` at θ = `π/6` is:
Simplest form of `tan^-1 ((sqrt(1 + cos "x") + sqrt(1 - cos "x"))/(sqrt(1 + cos "x") - sqrt(1 - cos "x")))`, `π < "x" < (3π)/2` is:
`"tan" (pi/4 + 1/2 "cos"^-1 "x") + "tan" (pi/4 - 1/2 "cos"^-1 "x") =` ____________.
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`
`"sin"^-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 = ________.
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 ∠EAB = ________.
`tan^-1 1/2 + tan^-1 2/11` is equal to
`sin^-1(1 - x) - 2sin^-1 x = pi/2`, tan 'x' is equal to
If `cos^-1(2/(3x)) + cos^-1(3/(4x)) = π/2(x > 3/4)`, then x is equal to ______.
If sin–1x + sin–1y + sin–1z = π, show that `x^2 - y^2 - z^2 + 2yzsqrt(1 - x^2) = 0`
