Advertisements
Advertisements
प्रश्न
If 4 cos−1 x + sin−1 x = π, then the value of x is
पर्याय
`2/3`
`1/sqrt2`
`sqrt3/2`
`2/sqrt3`
Advertisements
उत्तर
(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
संबंधित प्रश्न
Solve for x:
`2tan^(-1)(cosx)=tan^(-1)(2"cosec" x)`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
`sin^-1(sin (7pi)/6)`
Evaluate the following:
`cos^-1(cos4)`
Evaluate the following:
`tan^-1(tan pi/3)`
Evaluate the following:
`tan^-1(tan4)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Evaluate:
`cot(tan^-1a+cot^-1a)`
Evaluate:
`cos(sec^-1x+\text(cosec)^-1x)`,|x|≥1
If `sin^-1x+sin^-1y=pi/3` and `cos^-1x-cos^-1y=pi/6`, find the values of x and y.
`tan^-1 1/4+tan^-1 2/9=1/2cos^-1 3/2=1/2sin^-1(4/5)`
`tan^-1 1/7+2tan^-1 1/3=pi/4`
`2tan^-1 1/5+tan^-1 1/8=tan^-1 4/7`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
Solve the following equation for x:
`3sin^-1 (2x)/(1+x^2)-4cos^-1 (1-x^2)/(1+x^2)+2tan^-1 (2x)/(1-x^2)=pi/3`
Solve the following equation for x:
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
Write the value of
\[\cos^{- 1} \left( \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\].
Write the value of sin−1
\[\left( \sin( -{600}°) \right)\].
Write the value of sin \[\left\{ \frac{\pi}{3} - \sin^{- 1} \left( - \frac{1}{2} \right) \right\}\]
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the value of \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]
If 4 sin−1 x + cos−1 x = π, then what is the value of x?
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the principal value of `sin^-1(-1/2)`
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
If \[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\] , find the value of x.
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
The number of solutions of the equation \[\tan^{- 1} 2x + \tan^{- 1} 3x = \frac{\pi}{4}\] is
If x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] is equal to
If \[\cos^{- 1} \frac{x}{2} + \cos^{- 1} \frac{y}{3} = \theta,\] then 9x2 − 12xy cos θ + 4y2 is equal to
\[\cot\left( \frac{\pi}{4} - 2 \cot^{- 1} 3 \right) =\]
The domain of \[\cos^{- 1} \left( x^2 - 4 \right)\] is
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
Prove that : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
The value of tan `("cos"^-1 4/5 + "tan"^-1 2/3) =`
