Advertisements
Advertisements
प्रश्न
Prove the following:
3 sin−1 x = sin−1 (3x − 4x3), `x ∈ [-1/2, 1/2]`
Advertisements
उत्तर
Let x = sin θ.
Then, sin−1 x = θ.
We have,
R.H.S = sin−1 (3x – 4x3) = sin−1 (3 sin θ – 4 sin3θ)
= sin−1 (sin 3θ) = sin−1 (3 sin θ – 4 sin3θ)
= 3θ = sin−1 (3 sin θ – 4 sin3θ)
= 3 sin−1 x = sin−1 (3 sin θ – 4 sin3θ)
R.H.S = L.H.S
APPEARS IN
संबंधित प्रश्न
Prove that `2tan^(-1)(1/5)+sec^(-1)((5sqrt2)/7)+2tan^(-1)(1/8)=pi/4`
Prove that: `tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4`
Solve for x : tan-1 (x - 1) + tan-1x + tan-1 (x + 1) = tan-1 3x
If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.
Prove `tan^(-1) 2/11 + tan^(-1) 7/24 = tan^(-1) 1/2`
Find the value of the following:
`tan 1/2 [sin^(-1) (2x)/(1 + x^2) + cos^(-1) (1 - y^2)/(1 + y^2)], |x| < 1, y > 0 and xy < 1`
if `tan^(-1) (x-1)/(x - 2) + tan^(-1) (x + 1)/(x + 2) = pi/4` then find the value of x.
Find the value of the given expression.
`tan^(-1) (tan (3pi)/4)`
Find the value of the given expression.
`tan(sin^(-1) 3/5 + cot^(-1) 3/2)`
`cos^(-1) (cos (7pi)/6)` is equal to ______.
`sin[pi/3 - sin^(-1) (-1/2)]` is equal to ______.
Prove that `cos^(-1) 4/5 + cos^(-1) 12/13 = cos^(-1) 33/65`.
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`
Solve `tan^(-1) - tan^(-1) (x - y)/(x+y)` is equal to
(A) `pi/2`
(B). `pi/3`
(C) `pi/4`
(D) `(-3pi)/4`
Prove that
\[2 \tan^{- 1} \left( \frac{1}{5} \right) + \sec^{- 1} \left( \frac{5\sqrt{2}}{7} \right) + 2 \tan^{- 1} \left( \frac{1}{8} \right) = \frac{\pi}{4}\] .
Find the value of `cot[sin^-1 3/5 + sin^-1 4/5]`
Find the value of `tan(sin^-1 3/5 + cot^-1 3/2)`
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)`
Solve: `tan^-1x = cos^-1 (1 - "a"^2)/(1 + "a"^2) - cos^-1 (1 - "b"^2)/(1 + "b"^2), "a" > 0, "b" > 0`
Solve: `2tan^-1 (cos x) = tan^-1 (2"cosec" x)`
Find the number of solutions of the equation `tan^-1 (x - 1) + tan^-1x + tan^-1(x + 1) = tan^-1(3x)`
Choose the correct alternative:
`sin^-1 (tan pi/4) - sin^-1 (sqrt(3/x)) = pi/6`. Then x is a root of the equation
Evaluate tan (tan–1(– 4)).
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`
Show that `tan(1/2 sin^-1 3/4) = (4 - sqrt(7))/3` and justify why the other value `(4 + sqrt(7))/3` is ignored?
If |x| ≤ 1, then `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` is equal to ______.
If cos–1x > sin–1x, then ______.
The value of cot `("cosec"^-1 5/3 + "tan"^-1 2/3)` is ____________.
The value of sin (2tan-1 (0.75)) is equal to ____________.
If sin `("sin"^-1 1/5 + "cos"^-1 "x") = 1,` then the value of x is ____________.
The value of `"tan"^-1 (3/4) + "tan"^-1 (1/7)` is ____________.
What is the value of cos (sec–1x + cosec–1x), |x| ≥ 1
Find the value of `tan^-1 [2 cos (2 sin^-1 1/2)] + tan^-1 1`.
`tan^-1 sqrt3 - cot^-1 (- sqrt3)` is equal to ______.
Solve:
sin–1 (x) + sin–1 (1 – x) = cos–1 x
