Advertisements
Advertisements
प्रश्न
`sin^-1 1/2-2sin^-1 1/sqrt2`
उत्तर
`sin^-1 1/2-2sin^-1 1/sqrt2 =sin^-1 1/2-sin^-1 2xx1/sqrt2sqrt(1-(1/sqrt2)^2)`
`=sin^-1 1/2-sin^-1sqrt2xx1/sqrt2`
`=sin^-1 1/2-sin^-1 1`
`=sin^-1(sin pi/6)-sin^-1(sin pi/2)`
`=pi/6-pi/2`
`=-pi/3`
APPEARS IN
संबंधित प्रश्न
Show that `2sin^-1(3/5) = tan^-1(24/7)`
Find the principal value of tan−1 (−1)
Find the principal value of `cosec^(-1)(-sqrt2)`
`tan^(-1) sqrt3 - sec^(-1)(-2)` is equal to ______.
Find the domain of the following function:
`f(x) = sin^-1x + sinx`
Find the set of values of `cosec^-1(sqrt3/2)`
Evaluate the following:
`\text(cosec)^-1(-2/sqrt3)+2cot^-1(-1)`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of cosA
In ΔABC prove that `(b + c - a) tan "A"/(2) = (c + a - b)tan "B"/(2) = (a + b - c)tan "C"/(2)`.
Evaluate the following:
`tan^-1 sqrt(3) - sec^-1 (-2)`
Prove the following:
`tan^-1["cosθ + sinθ"/"cosθ - sinθ"] = pi/(4) + θ, if θ ∈ (- pi/4, pi/4)`
Prove the following:
`tan^-1[sqrt((1 - cosθ)/(1 + cosθ))] = θ/(2)`, if θ ∈ (– π, π).
In ΔABC, prove the following:
`(cos A)/a + (cos B)/b + (cos C)/c = (a^2 + b^2 + c^2)/(2abc)`
Evaluate cot(tan−1(2x) + cot−1(2x))
Find the value of `cos^-1 (1/2) + tan^-1 (1/sqrt(3))`
Prove that cot−1(7) + 2 cot−1(3) = `pi/4`
Find the principal value of the following:
`sin^-1 (- 1/2)`
Evaluate: sin`[1/2 cos^-1 (4/5)]`
Express `tan^-1 ((cos x - sin x)/(cos x + sin x))`, 0 < x < π in the simplest form.
Find the principal value of `tan^-1 (sqrt(3))`
If `sin^-1(x/13) + cosec^-1(13/12) = pi/2`, then the value of x is ______
The principal value of `sin^-1 (sin (3pi)/4)` is ______.
In a triangle ABC, ∠C = 90°, then the value of `tan^-1 ("a"/("b + c")) + tan^-1("b"/("c + a"))` is ______.
`cos^-1 4/5 + tan^-1 3/5` = ______.
Show that `cos(2tan^-1 1/7) = sin(4tan^-1 1/3)`
Show that `sin^-1 5/13 + cos^-1 3/5 = tan^-1 63/16`
If `"cos"^-1 "x + sin"^-1 "x" = pi`, then the value of x is ____________.
`2 "tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
If `"sin"^-1("x"^2 - 7"x" + 12) = "n"pi, AA "n" in "I"`, then x = ____________.
`"tan"^-1 sqrt3 - "sec"^-1 (-2)` is equal to ____________.
sin 6θ + sin 4θ + sin 2θ = 0, then θ =
`2tan^-1 (cos x) = tan^-1 (2"cosec" x)`, then 'x' will be equal to
Assertion (A): The domain of the function sec–12x is `(-∞, - 1/2] ∪ pi/2, ∞)`
Reason (R): sec–1(–2) = `- pi/4`
`cot^-1(sqrt(cos α)) - tan^-1 (sqrt(cos α))` = x, then sin x = ______.
If sin–1a + sin–1b + sin–1c = π, then find the value of `asqrt(1 - a^2) + bsqrt(1 - b^2) + csqrt(1 - c^2)`.
Prove that:
tan–1x + tan–1y = `π + tan^-1((x + y)/(1 - xy))`, provided x > 0, y > 0, xy > 1
Solve for x:
5tan–1x + 3cot–1x = 2π
