Advertisements
Advertisements
प्रश्न
Evaluate sin \[\left( \tan^{- 1} \frac{3}{4} \right)\]
Advertisements
उत्तर
We know that
\[\tan^{- 1} x = \sin^{- 1} \frac{x}{\sqrt{1 + x^2}}\]
\[\therefore \sin\left( \tan^{- 1} \frac{3}{4} \right) = \sin\left\{ \sin^{- 1} \left( \frac{\frac{3}{4}}{\sqrt{1 + \frac{9}{16}}} \right) \right\}\]
\[ = \sin\left\{ \sin^{- 1} \left( \frac{\frac{3}{4}}{\frac{5}{4}} \right) \right\}\]
\[ = \sin\left( \sin^{- 1} \frac{3}{5} \right)\]
\[ = \frac{3}{5} \left[ \because \sin\left( \sin^{- 1} x \right) = x \right]\]
∴ \[\sin\left( \tan^{- 1} \frac{3}{4} \right) = \frac{3}{5}\]
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+tan-1y=π/4,xy<1, then write the value of x+y+xy.
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)=cos^-1x+cosx.`
Find the principal values of the following:
`cos^-1(-1/sqrt2)`
`sin^-1(sin12)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`tan^-1(tan pi/3)`
Evaluate the following:
`tan^-1(tan12)`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`sec^-1(sec (5pi)/4)`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
`sin^-1x=pi/6+cos^-1x`
`tan^-1x+2cot^-1x=(2x)/3`
Prove the following result:
`tan^-1 1/4+tan^-1 2/9=sin^-1 1/sqrt5`
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((x-2)/(x-4))+tan^-1((x+2)/(x+4))=pi/4`
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
`2sin^-1 3/5-tan^-1 17/31=pi/4`
Prove that
`sin{tan^-1 (1-x^2)/(2x)+cos^-1 (1-x^2)/(2x)}=1`
Find the value of the following:
`tan^-1{2cos(2sin^-1 1/2)}`
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
Write the value of sin−1 \[\left( \cos\frac{\pi}{9} \right)\]
Write the principal value of \[\cos^{- 1} \left( \cos\frac{2\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{2\pi}{3} \right)\]
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
Wnte the value of\[\cos\left( \frac{\tan^{- 1} x + \cot^{- 1} x}{3} \right), \text{ when } x = - \frac{1}{\sqrt{3}}\]
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is
\[\text{ If } u = \cot^{- 1} \sqrt{\tan \theta} - \tan^{- 1} \sqrt{\tan \theta}\text{ then }, \tan\left( \frac{\pi}{4} - \frac{u}{2} \right) =\]
It \[\tan^{- 1} \frac{x + 1}{x - 1} + \tan^{- 1} \frac{x - 1}{x} = \tan^{- 1}\] (−7), then the value of x is
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
If x > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
Find the domain of `sec^(-1)(3x-1)`.
Find the value of `sin^-1(cos((33π)/5))`.
