Advertisements
Advertisements
प्रश्न
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
Advertisements
उत्तर
We know
`sin^-1x+sin^-1y=sin^-1[xsqrt(1-y^2)+ysqrt(1-x^2)]`
∴ `sin^-1x+sin^-1 2x=pi/3`
⇒ `sin^-1x+sin^-1 2x=sin^-1(sqrt3/2)`
⇒ `sin^-1x-sin^-1(sqrt3/2)=-sin^-1 2x`
⇒ `sin^-1[xsqrt(1-3/4)+sqrt3/2sqrt(1-x^2)]=-sin^-1 2x`
⇒ `sin^-1[x/2+sqrt3/2sqrt(1-x^2)]=sin^-1(-2x)`
⇒ `x/2+sqrt3/2sqrt(1-x^2)=-2x`
⇒ `x+sqrt3sqrt(1-x^2)=-4x`
⇒ `5x=-sqrt3sqrt(1-x^2)`
Squaring both the sides,
`25x^2=3-3x^2`
⇒ `28x^2=3`
⇒ `x=+-1/2sqrt(3/7)`
APPEARS IN
संबंधित प्रश्न
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
`sin^-1(sin4)`
Evaluate the following:
`tan^-1(tan pi/3)`
Evaluate the following:
`tan^-1(tan (7pi)/6)`
Evaluate the following:
`sec^-1(sec (7pi)/3)`
Evaluate the following:
`sec^-1(sec (13pi)/4)`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Evaluate the following:
`sin(sec^-1 17/8)`
Evaluate the following:
`cot(cos^-1 3/5)`
Evaluate the following:
`cos(tan^-1 24/7)`
Evaluate:
`sec{cot^-1(-5/12)}`
If `(sin^-1x)^2+(cos^-1x)^2=(17pi^2)/36,` Find x
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
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`
`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`
`tan^-1 1/4+tan^-1 2/9=1/2cos^-1 3/2=1/2sin^-1(4/5)`
`2tan^-1 1/5+tan^-1 1/8=tan^-1 4/7`
Solve the following equation for x:
`2tan^-1(sinx)=tan^-1(2sinx),x!=pi/2`
Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
Write the value of tan−1 x + tan−1 `(1/x)` for x < 0.
Evaluate sin \[\left( \tan^{- 1} \frac{3}{4} \right)\]
Write the value of cos−1 (cos 350°) − sin−1 (sin 350°)
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
If \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find x.
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`
Write the value of \[\sec^{- 1} \left( \frac{1}{2} \right)\]
If \[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\] , find the value of x.
If sin−1 x − cos−1 x = `pi/6` , then x =
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] is equal to
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
The domain of \[\cos^{- 1} \left( x^2 - 4 \right)\] is
Write the value of \[\cos^{- 1} \left( - \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\] .
Find the value of `sin^-1(cos((33π)/5))`.
