Advertisements
Advertisements
प्रश्न
Evaluate the following:
`sin(cos^-1 5/13)`
उत्तर
`sin(cos^-1 5/13)=sin(sin^-1sqrt(1-(5/13)^2))` `[thereforecos^-1x=sin^-1sqrt(1-x^2)]`
`=sin[sin^-1(sqrt(1-25/169))]`
`=sin[sin^-1(sqrt(144/169))]`
`=sin[sin^-1 12/13]`
`=12/13`
APPEARS IN
संबंधित प्रश्न
If `(sin^-1x)^2 + (sin^-1y)^2+(sin^-1z)^2=3/4pi^2,` find the value of x2 + y2 + z2
`sin^-1{(sin - (17pi)/8)}`
Evaluate the following:
`cos^-1{cos ((4pi)/3)}`
Evaluate the following:
`sec^-1(sec (7pi)/3)`
Evaluate the following:
`cosec^-1(cosec (3pi)/4)`
Evaluate the following:
`cosec^-1(cosec (11pi)/6)`
Write the following in the simplest form:
`tan^-1sqrt((a-x)/(a+x)),-a<x<a`
Write the following in the simplest form:
`sin^-1{(sqrt(1+x)+sqrt(1-x))/2},0<x<1`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Evaluate:
`cot{sec^-1(-13/5)}`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
Evaluate:
`cot(tan^-1a+cot^-1a)`
Solve the following equation for x:
tan−1(x + 1) + tan−1(x − 1) = tan−1`8/31`
Solve the following equation for x:
tan−1(x + 2) + tan−1(x − 2) = tan−1 `(8/79)`, x > 0
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
`2sin^-1 3/5-tan^-1 17/31=pi/4`
`2tan^-1(1/2)+tan^-1(1/7)=tan^-1(31/17)`
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=pi/2`
Solve the following equation for x:
`tan^-1((2x)/(1-x^2))+cot^-1((1-x^2)/(2x))=(2pi)/3,x>0`
If `sin^-1x+sin^-1y+sin^-1z=(3pi)/2,` then write the value of x + y + z.
Write the value of tan−1 x + tan−1 `(1/x)` for x < 0.
If −1 < x < 0, then write the value of `sin^-1((2x)/(1+x^2))+cos^-1((1-x^2)/(1+x^2))`
Write the value of sin−1 \[\left( \cos\frac{\pi}{9} \right)\]
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
Write the principal value of \[\cos^{- 1} \left( \cos680^\circ \right)\]
Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
Find the value of \[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right)\]
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 x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals
It \[\tan^{- 1} \frac{x + 1}{x - 1} + \tan^{- 1} \frac{x - 1}{x} = \tan^{- 1}\] (−7), then the value of x 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
The period of the function f(x) = tan3x is ____________.
Solve for x : {xcos(cot-1 x) + sin(cot-1 x)}2 = `51/50`