Advertisements
Advertisements
प्रश्न
Let f (x) = `e^(cos^-1){sin(x+pi/3}.`
Then, f (8π/9) =
पर्याय
e5π/18
e13π/18
e−2π/18
none of these
Advertisements
उत्तर
(b) e13π/18
Given: \[f\left( x \right) = e^{\cos^{- 1}} \left\{ \sin\left( x + \frac{\pi}{3} \right) \right\}\]
Then,
\[f\left( \frac{8\pi}{9} \right) = e^{\cos^{- 1}} \left\{ \sin\left( \frac{8\pi}{9} + \frac{\pi}{3} \right) \right\} \]
\[ = e^{\cos^{- 1}} \left\{ \sin\left( \frac{11\pi}{9} \right) \right\} \]
\[ = e^{\cos^{- 1}} \left\{ \cos\left( \frac{\pi}{2} + \frac{13\pi}{18} \right) \right\} \left[ \because \cos\left( \frac{\pi}{2} + \theta \right) = \sin\theta \right]\]
\[ = e^{\cos^{- 1}} \left\{ \cos\left( \frac{13\pi}{18} \right) \right\} \]
\[ = e^\frac{13\pi}{18}\]
APPEARS IN
संबंधित प्रश्न
Prove that :
`2 tan^-1 (sqrt((a-b)/(a+b))tan(x/2))=cos^-1 ((a cos x+b)/(a+b cosx))`
If (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy.
`sin^-1(sin (5pi)/6)`
`sin^-1(sin (13pi)/7)`
`sin^-1(sin2)`
Evaluate the following:
`cos^-1(cos3)`
Evaluate the following:
`tan^-1(tan1)`
Evaluate the following:
`sec^-1(sec (13pi)/4)`
Evaluate the following:
`cosec^-1(cosec (11pi)/6)`
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)-1)/x},x !=0`
Evaluate the following:
`cos(tan^-1 24/7)`
Evaluate:
`cosec{cot^-1(-12/5)}`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
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:
`tan^-1((x-2)/(x-4))+tan^-1((x+2)/(x+4))=pi/4`
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
`sin^-1 4/5+2tan^-1 1/3=pi/2`
Solve the following equation for x:
`2tan^-1(sinx)=tan^-1(2sinx),x!=pi/2`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
If `sin^-1x+sin^-1y+sin^-1z=(3pi)/2,` then write the value of x + y + z.
Write the range of tan−1 x.
Write the value of sin−1 (sin 1550°).
Write the value of cos−1 \[\left( \tan\frac{3\pi}{4} \right)\]
Write the value of cos−1 (cos 350°) − sin−1 (sin 350°)
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the principal value of `sin^-1(-1/2)`
Write the principal value of \[\cos^{- 1} \left( \cos680^\circ \right)\]
If α = \[\tan^{- 1} \left( \frac{\sqrt{3}x}{2y - x} \right), \beta = \tan^{- 1} \left( \frac{2x - y}{\sqrt{3}y} \right),\]
then α − β =
The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is
sin \[\left\{ 2 \cos^{- 1} \left( \frac{- 3}{5} \right) \right\}\] is equal to
The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] is
The domain of \[\cos^{- 1} \left( x^2 - 4 \right)\] is
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
tanx is periodic with period ____________.
