Advertisements
Advertisements
Question
`sin^-1(sin4)`
Advertisements
Solution
`sin^-1(sin4) = y`
`y = [-pi/2, pi/2]`
sin (4) = sin (y) → y = 4 → x
sin (4 − π + π)
sin (π + (4 − π))
−sin (4 − π)
sin (−(4 − π))
sin (π − 4) = sin (y)
y = π − 4
APPEARS IN
RELATED QUESTIONS
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
`sin^-1(sin pi/6)`
`sin^-1(sin (5pi)/6)`
Evaluate the following:
`tan^-1(tan (6pi)/7)`
Evaluate the following:
`tan^-1(tan (9pi)/4)`
Evaluate the following:
`tan^-1(tan12)`
Evaluate the following:
`sec^-1(sec (25pi)/6)`
Evaluate the following:
`cosec^-1{cosec (-(9pi)/4)}`
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)+1)/x},x !=0`
Write the following in the simplest form:
`tan^-1sqrt((a-x)/(a+x)),-a<x<a`
Evaluate the following:
`cosec(cos^-1 3/5)`
Evaluate the following:
`tan(cos^-1 8/17)`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x < 0
If `sin^-1x+sin^-1y=pi/3` and `cos^-1x-cos^-1y=pi/6`, find the values of x and y.
`sin(sin^-1 1/5+cos^-1x)=1`
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
Solve the following equation for x:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
Prove that:
`2sin^-1 3/5=tan^-1 24/7`
`tan^-1 1/4+tan^-1 2/9=1/2cos^-1 3/2=1/2sin^-1(4/5)`
Find the value of the following:
`tan^-1{2cos(2sin^-1 1/2)}`
Solve the following equation for x:
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
Write the value of tan−1 x + tan−1 `(1/x)` for x < 0.
Write the value of cos−1 (cos 1540°).
Write the value of \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]
If \[\sin^{- 1} \left( \frac{1}{3} \right) + \cos^{- 1} x = \frac{\pi}{2},\] then find x.
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the value of \[\sec^{- 1} \left( \frac{1}{2} \right)\]
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
Write the value of \[\tan^{- 1} \left( \frac{1}{x} \right)\] for x < 0 in terms of `cot^-1x`
If \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} - \sqrt{1 - x^2}}{\sqrt{1 + x^2} + \sqrt{1 - x^2}} \right)\] = α, then x2 =
If sin−1 x − cos−1 x = `pi/6` , then x =
The number of real solutions of the equation \[\sqrt{1 + \cos 2x} = \sqrt{2} \sin^{- 1} (\sin x), - \pi \leq x \leq \pi\]
The value of \[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right)\] is
If \[\sin^{- 1} \left( \frac{2a}{1 - a^2} \right) + \cos^{- 1} \left( \frac{1 - a^2}{1 + a^2} \right) = \tan^{- 1} \left( \frac{2x}{1 - x^2} \right),\text{ where }a, x \in \left( 0, 1 \right)\] , then, the value of x is
If \[\tan^{- 1} \left( \frac{1}{1 + 1 . 2} \right) + \tan^{- 1} \left( \frac{1}{1 + 2 . 3} \right) + . . . + \tan^{- 1} \left( \frac{1}{1 + n . \left( n + 1 \right)} \right) = \tan^{- 1} \theta\] , then find the value of θ.
Find the domain of `sec^(-1)(3x-1)`.
Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
Solve for x : {xcos(cot-1 x) + sin(cot-1 x)}2 = `51/50`
