Advertisements
Advertisements
Question
Prove the following:
3cos−1x = cos−1(4x3 − 3x), `x ∈ [1/2, 1]`
Advertisements
Solution
Let x = cos θ
Then, cos−1x = θ
We have,
R.H.S = cos−1(4x3 − 3x)
⇒ cos−1(4 cos3θ − 3 cos θ)
⇒ cos−1(cos 3θ) = cos−1(4x3 − 3x)
⇒ 3θ = cos−1(4x3 − 3x)
⇒ 3 cos−1x = cos−1(4x3 − 3x)
R.H.S = L.H.S
APPEARS IN
RELATED QUESTIONS
Prove that `cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2;x in (0,pi/4) `
If `tan^-1(2x)+tan^-1(3x)=pi/4`, then find the value of ‘x’.
Write the following function in the simplest form:
`tan^(-1) (sqrt(1+x^2) -1)/x`, x ≠ 0
Find the value of the following:
`tan^-1 [2 cos (2 sin^-1 1/2)]`
Find the value of `cot(tan^(-1) a + cot^(-1) a)`
if `sin(sin^(-1) 1/5 + cos^(-1) x) = 1` then find the value of x
Find the value of the given expression.
`tan^(-1) (tan (3pi)/4)`
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 `3sin^(-1)x = sin^(-1) (3x - 4x^3)`, `x in [-1/2, 1/2]`
Solve for x : \[\tan^{- 1} \left( \frac{x - 2}{x - 1} \right) + \tan^{- 1} \left( \frac{x + 2}{x + 1} \right) = \frac{\pi}{4}\] .
Find: ∫ sin x · log cos x dx
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 [sin 5]`
Find the value of the expression in terms of x, with the help of a reference triangle
sin (cos–1(1 – x))
Find the value of `sin^-1[cos(sin^-1 (sqrt(3)/2))]`
Find the value of `tan(sin^-1 3/5 + cot^-1 3/2)`
Prove that `sin^-1 3/5 - cos^-1 12/13 = sin^-1 16/65`
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^-1(sin((-pi)/2))`.
Evaluate `cos[cos^-1 ((-sqrt(3))/2) + pi/6]`
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 3 tan–1x + cot–1x = π, then x equals ______.
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 |x| ≤ 1, then `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` is equal to ______.
The minimum value of sinx - cosx is ____________.
If `"tan"^-1 ("cot" theta) = 2theta, "then" theta` is equal to ____________.
`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`
The value of sin (2tan-1 (0.75)) is equal to ____________.
If tan-1 2x + tan-1 3x = `pi/4,` then x is ____________.
sin (tan−1 x), where |x| < 1, is equal to:
If x = a sec θ, y = b tan θ, then `("d"^2"y")/("dx"^2)` at θ = `π/6` is:
`"tan" (pi/4 + 1/2 "cos"^-1 "x") + "tan" (pi/4 - 1/2 "cos"^-1 "x") =` ____________.
If `"sin"^-1 (1 - "x") - 2 "sin"^-1 ("x") = pi/2,` then x is equal to ____________.
If `3 "sin"^-1 ((2"x")/(1 + "x"^2)) - 4 "cos"^-1 ((1 - "x"^2)/(1 + "x"^2)) + 2 "tan"^-1 ((2"x")/(1 - "x"^2)) = pi/3` then x is equal to ____________.
Solve for x : `{"x cos" ("cot"^-1 "x") + "sin" ("cot"^-1 "x")}^2` = `51/50
The value of `tan^-1 (x/y) - tan^-1 (x - y)/(x + y)` is equal to
Find the value of `sin^-1 [sin((13π)/7)]`
Find the value of `tan^-1 [2 cos (2 sin^-1 1/2)] + tan^-1 1`.
