Advertisements
Advertisements
Question
If 4 cos−1 x + sin−1 x = π, then the value of x is
Options
`2/3`
`1/sqrt2`
`sqrt3/2`
`2/sqrt3`
Advertisements
Solution
(c) `sqrt3/2`
We know that
\[\sin^{- 1} x + \cos^{- 1} x = \frac{\pi}{2}\]
\[4 \cos^{- 1} x + \sin^{- 1} x = \pi\]
\[ \Rightarrow 4 \cos^{- 1} x + \frac{\pi}{2} - \cos^{- 1} x = \pi\]
\[ \Rightarrow 3 \cos^{- 1} x = \pi - \frac{\pi}{2}\]
\[ \Rightarrow 3 \cos^{- 1} x = \frac{\pi}{2}\]
\[ \Rightarrow \cos^{- 1} x = \frac{\pi}{6}\]
\[ \Rightarrow x = \cos\frac{\pi}{6}\]
\[ \Rightarrow x = \frac{\sqrt{3}}{2}\]
APPEARS IN
RELATED QUESTIONS
Write the value of `tan(2tan^(-1)(1/5))`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
If `tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4` ,find the value of x
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
`sin^-1(sin3)`
Evaluate the following:
`cos^-1{cos ((4pi)/3)}`
Evaluate the following:
`cos^-1(cos3)`
Evaluate the following:
`tan^-1(tan pi/3)`
Evaluate the following:
`sec^-1(sec (13pi)/4)`
Evaluate the following:
`sec^-1(sec (25pi)/6)`
Evaluate the following:
`\text(cosec)^-1(\text{cosec} pi/4)`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Evaluate the following:
`cos(tan^-1 24/7)`
If `sin^-1x+sin^-1y=pi/3` and `cos^-1x-cos^-1y=pi/6`, find the values of x and y.
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
Find the value of `tan^-1 (x/y)-tan^-1((x-y)/(x+y))`
Solve the following equation for x:
`tan^-1((1-x)/(1+x))-1/2 tan^-1x` = 0, where x > 0
Solve the following equation for x:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
Solve the following equation for x:
tan−1(x + 2) + tan−1(x − 2) = tan−1 `(8/79)`, x > 0
Solve the following equation for x:
`tan^-1(2+x)+tan^-1(2-x)=tan^-1 2/3, where x< -sqrt3 or, x>sqrt3`
`sin^-1 63/65=sin^-1 5/13+cos^-1 3/5`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
If `sin^-1 (2a)/(1+a^2)-cos^-1 (1-b^2)/(1+b^2)=tan^-1 (2x)/(1-x^2)`, then prove that `x=(a-b)/(1+ab)`
Solve the following equation for x:
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
If `sin^-1x+sin^-1y+sin^-1z=(3pi)/2,` then write the value of x + y + z.
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
Write the value of cos−1 (cos 350°) − sin−1 (sin 350°)
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the value of \[\tan^{- 1} \left( \frac{1}{x} \right)\] for x < 0 in terms of `cot^-1x`
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
\[\text{ If }\cos^{- 1} \frac{x}{3} + \cos^{- 1} \frac{y}{2} = \frac{\theta}{2}, \text{ then }4 x^2 - 12xy \cos\frac{\theta}{2} + 9 y^2 =\]
If θ = sin−1 {sin (−600°)}, then one of the possible values of θ is
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
Prove that : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
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`
