Advertisements
Advertisements
Question
Find the principal value of the following: cosec- 1(2)
Solution
The principal value branch of cosec-1x is `[- pi/2, pi/2] - {0}`.
Let cosec-1(2) = α, `"where" (-pi)/(2) ≤ α ≤ pi/(2)`, α ≠ 0.
∴ cosec α = 2 = `"cosec" pi/(6)`
∴ α = `pi/(6) ...[ ∵ - pi/2 ≤ pi/6 ≤ pi/2 ]`
∴ the principal value of cosec-1(2) is `pi/(6)`.
APPEARS IN
RELATED QUESTIONS
If `tan^-1((x-1)/(x-2))+cot^-1((x+2)/(x+1))=pi/4; `
Find the principal value of `cosec^(-1)(-sqrt2)`
Find the value of the following:
`tan^(-1) (tan (7x)/6)`
Find the principal value of `sin^-1(1/sqrt2)`
`sin^-1{cos(sin^-1 sqrt3/2)}`
Find the domain of the following function:
`f(x)=sin^-1x+sin^-1 2x`
Find the domain of `f(x)=cotx+cot^-1x`
Evaluate the following:
`\text(cosec)^-1(-2/sqrt3)+2cot^-1(-1)`
Find the principal value of the following: `sin^-1 (1/2)`
Find the principal value of the following: tan- 1( - √3)
Evaluate the following:
`tan^-1(1) + cos^-1(1/2) + sin^-1(1/2)`
Prove the following:
`tan^-1["cosθ + sinθ"/"cosθ - sinθ"] = pi/(4) + θ, if θ ∈ (- pi/4, pi/4)`
Find the principal solutions of the following equation:
sin 2θ = `− 1/(sqrt2)`
Find the principal solutions of the following equation:
tan 5θ = -1
sin−1x − cos−1x = `pi/6`, then x = ______
The principal value of sin−1`(1/2)` is ______
The principal value of cos−1`(-1/2)` is ______
Evaluate cot(tan−1(2x) + cot−1(2x))
Prove that cot−1(7) + 2 cot−1(3) = `pi/4`
Prove that `2 tan^-1 (1/8) + tan^-1 (1/7) + 2tan^-1 (1/5) = pi/4`
Find the principal value of the following:
`sin^-1 (- 1/2)`
Prove that:
`tan^-1 (4/3) + tan^-1 (1/7) = pi/4`
Solve `tan^-1 2x + tan^-1 3x = pi/4`
Evaluate:
`cos[tan^-1 (3/4)]`
Evaluate: `cos (sin^-1 (4/5) + sin^-1 (12/13))`
Express `tan^-1 [(cos x)/(1 - sin x)], - pi/2 < x < (3pi)/2` in the simplest form.
Find the principal value of `sec^-1 (- sqrt(2))`
Find the principal value of `tan^-1 (sqrt(3))`
A man standing directly opposite to one side of a road of width x meter views a circular shaped traffic green signal of diameter ‘a’ meter on the other side of the road. The bottom of the green signal Is ‘b’ meter height from the horizontal level of viewer’s eye. If ‘a’ denotes the angle subtended by the diameter of the green signal at the viewer’s eye, then prove that α = `tan^-1 (("a" + "b")/x) - tan^-1 ("b"/x)`
The value of cot `(tan^-1 2x + cot^-1 2x)` is ______
In ΔABC, tan`A/2 = 5/6` and tan`C/2 = 2/5`, then ______
If 2tan-1 (cos x) = tan-1 (cosec2 x), then x = ______.
In a triangle ABC, ∠C = 90°, then the value of `tan^-1 ("a"/("b + c")) + tan^-1("b"/("c + a"))` is ______.
If `3sin^-1((2x)/(1 + x^2)) - 4cos^-1((1 - x^2)/(1 + x^2)) + 2tan^-1((2x)/(1 - x^2)) = pi/3`, then x is equal to ______
`(sin^-1(-1/2) + tan^-1(-1/sqrt(3)))/(sec^-1 (-2/sqrt(3)) + cos^-1(1/sqrt(2))` = ______.
If `3tan^-1x +cot^-1x = pi`, then xis equal to ______.
The value of `sin^-1[cos(pi/3)] + sin^-1[tan((5pi)/4)]` is ______.
The equation tan–1x – cot–1x = `(1/sqrt(3))` has ______.
Prove that `tan^-1 1/4 + tan^-1 2/9 = sin^-1 1/sqrt(5)`
All trigonometric functions have inverse over their respective domains.
If `"cos"^-1 "x + sin"^-1 "x" = pi`, then the value of x is ____________.
`"sin"^-1 (1/sqrt2)`
`2 "tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
`"sin" ["cot"^-1 {"cos" ("tan"^-1 "x")}] =` ____________.
The value of `"cos"^-1 ("cos" ((33 pi)/5))` is ____________.
`"tan"(pi/4 + 1/2 "cos"^-1 "x") + "tan" (pi/4 - 1/2 "cos"^-1 "x") =` ____________.
3 tan-1 a is equal to ____________.
`sin[π/3 - sin^-1 (-1/2)]` is equal to:
`"cos" ["tan"^-1 {"sin" ("cot"^-1 "x")}]` is equal to ____________.
`"cos"^-1 ("cos" ((7pi)/6))` is equal to ____________.
The equation of the tangent to the curve given by x = a sin3t, y = bcos3t at a point where t = `pi/2` is
Which of the following functions is inverse of itself?
The number of solutions of sin–1x + sin–1(1 – x) = cos–1x is
sin 6θ + sin 4θ + sin 2θ = 0, then θ =
If `(-1)/sqrt(2) ≤ x ≤ 1/sqrt(2)` then `sin^-1 (2xsqrt(1 - x^2))` is equal to
Find the principal value of `tan^-1 (sqrt(3))`
Values of tan–1 – sec–1(–2) is equal to
`sin(tan^-1x), |x| < 1` is equal to
`2tan^-1 (cos x) = tan^-1 (2"cosec" x)`, then 'x' will be equal to
If `sin(sin^-1 1/5 + cos^-1 x) = 1`, the what will be the value of x?
Assertion (A): The domain of the function sec–12x is `(-∞, - 1/2] ∪ pi/2, ∞)`
Reason (R): sec–1(–2) = `- pi/4`
If θ = `sin^-1((2x)/(1 + x^2)) + cos^-1((1 - x^2)/(1 + x^2))`, for `x ≥ 3/2` then the absolute value of `((cosθ + tanθ + 4)/secθ)` is ______.
Number of values of x satisfying the system of equations `sin^-1sqrt(2 + e^(-2x) - 2e^-x) + sec^-1sqrt(1 - x^2 + x^4) = π/2` and `5^(1+tan^-1x)` = 4 + [cos–1x] is ______ (where [.] denotes greatest integer function)
`(tan^-1 (sqrt(3)) - sec^-1(-2))/("cosec"^-1(-sqrt(2)) + cos^-1(-1/2))` is equal to ______.
sin [cot–1 (cos (tan–1 x))] = ______.
If y = `tan^-1 (sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2))`, then `dy/dx` is equal to ______.
If sin–1x – cos–1x = `π/6`, then x = ______.
Find the value of `sin(2cos^-1 sqrt(5)/3)`.
