Advertisements
Advertisements
प्रश्न
Find the principal value of `tan^-1 (sqrt(3))`
उत्तर
Let y = `tan^-1 (sqrt(3))`
Where `- pi/2 ≤ y ≤ pi/2`
tan y = `sqrt(3)`
= `tan (pi/3)`
y = `pi/3`
∴ The principal value of `tan^-1 (sqrt(3)) = pi/3`
APPEARS IN
संबंधित प्रश्न
Prove that:
`tan^-1 ((sqrt(1 + x) - sqrt(1 - x))/(sqrt(1 + x) + sqrt(1 - x))) = pi/4 - 1/2 cos^-1 x`, for `- 1/sqrt2 <= x <= 1`
[Hint: put x = cos 2θ]
Find the domain of the following function:
`f(x)sin^-1sqrt(x^2-1)`
Find the principal value of the following: `sin^-1 (1/2)`
Show that `sin^-1(3/5) + sin^-1(8/17) = cos^-1(36/85)`
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 ______
In Δ ABC, with the usual notations, if sin B sin C = `"bc"/"a"^2`, then the triangle is ______.
If sin `(sin^-1 1/3 + cos^-1 x) = 1`, then the value of x is ______.
The value of cot (- 1110°) is equal to ______.
The value of `sin^-1(cos (53pi)/5)` is ______
`cos^-1 4/5 + tan^-1 3/5` = ______.
If 2 tan–1(cos θ) = tan–1(2 cosec θ), then show that θ = π 4, where n is any integer.
`"cos"^-1 1/2 + 2 "sin"^-1 1/2` is equal to ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
If `(-1)/sqrt(2) ≤ x ≤ 1/sqrt(2)` then `sin^-1 (2xsqrt(1 - x^2))` is equal to
Find the principal value of `cot^-1 ((-1)/sqrt(3))`
If x ∈ R – {0}, then `tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2)))`
Find the value of `tan^-1(x/y) + tan^-1((y - x)/(y + x))`
