Advertisements
Advertisements
Question
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 [sin 5]`
Solution
`- pi/2 ≤ sin^-1 5 ≤ pi/2`
`- 3 pi/2 ≤ 5 ≤ 2pi`
`- pi/2 ≤ 5 - 2pi ≤ 0 ≤ pi/2`
sin(5 – 2π) = sin 5
sin–1(sin 5) = 5 – 2π
APPEARS IN
RELATED QUESTIONS
Prove that `2tan^(-1)(1/5)+sec^(-1)((5sqrt2)/7)+2tan^(-1)(1/8)=pi/4`
Prove the following:
`3cos^(-1) x = cos^(-1)(4x^3 - 3x), x in [1/2, 1]`
`sin[pi/3 - sin^(-1) (-1/2)]` is equal to ______.
sin–1 (1 – x) – 2 sin–1 x = `pi/2` , then x is equal to ______.
Prove that `tan {pi/4 + 1/2 cos^(-1) a/b} + tan {pi/4 - 1/2 cos^(-1) a/b} = (2b)/a`
Solve for x : `tan^-1 ((2-"x")/(2+"x")) = (1)/(2)tan^-1 ("x")/(2), "x">0.`
Simplify: `tan^-1 x/y - tan^-1 (x - y)/(x + y)`
Choose the correct alternative:
`sin^-1 3/5 - cos^-1 13/13 + sec^-1 5/3 - "cosec"^-1 13/12` is equal to
Choose the correct alternative:
`sin^-1 (tan pi/4) - sin^-1 (sqrt(3/x)) = pi/6`. Then x is a root of the equation
Choose the correct alternative:
sin–1(2 cos2x – 1) + cos–1(1 – 2 sin2x) =
Solve the equation `sin^-1 6x + sin^-1 6sqrt(3)x = - pi/2`
Show that `2tan^-1 {tan alpha/2 * tan(pi/4 - beta/2)} = tan^-1 (sin alpha cos beta)/(cosalpha + sinbeta)`
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`
If `"sec" theta = "x" + 1/(4 "x"), "x" in "R, x" ne 0,`then the value of `"sec" theta + "tan" theta` is ____________.
The value of `"tan"^-1 (1/2) + "tan"^-1 (1/3) + "tan"^-1 (7/8)` is ____________.
If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt"cos" alpha) = "x",` the sinx is equal to ____________.
The value of the expression tan `(1/2 "cos"^-1 2/sqrt3)`
The value of `tan^-1 (x/y) - tan^-1 (x - y)/(x + y)` is equal to
`sin^-1(1 - x) - 2sin^-1 x = pi/2`, tan 'x' is equal to
`tan(2tan^-1 1/5 + sec^-1 sqrt(5)/2 + 2tan^-1 1/8)` is equal to ______.