Advertisements
Advertisements
प्रश्न
Evaluate sin \[\left( \tan^{- 1} \frac{3}{4} \right)\]
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
If `cos^-1( x/a) +cos^-1 (y/b)=alpha` , prove that `x^2/a^2-2(xy)/(ab) cos alpha +y^2/b^2=sin^2alpha`
Solve the following for x:
`sin^(-1)(1-x)-2sin^-1 x=pi/2`
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
`sin^-1(sin4)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`tan^-1(tan (9pi)/4)`
Evaluate the following:
`tan^-1(tan2)`
Write the following in the simplest form:
`sin^-1{(sqrt(1+x)+sqrt(1-x))/2},0<x<1`
Evaluate the following:
`sin(sin^-1 7/25)`
Evaluate the following:
`sin(tan^-1 24/7)`
Evaluate the following:
`cosec(cos^-1 3/5)`
Evaluate:
`cos{sin^-1(-7/25)}`
If `(sin^-1x)^2+(cos^-1x)^2=(17pi^2)/36,` Find x
`tan^-1x+2cot^-1x=(2x)/3`
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
Solve the following equation for x:
tan−1(x + 2) + tan−1(x − 2) = tan−1 `(8/79)`, x > 0
Solve `cos^-1sqrt3x+cos^-1x=pi/2`
Evaluate the following:
`tan 1/2(cos^-1 sqrt5/3)`
`tan^-1 1/4+tan^-1 2/9=1/2cos^-1 3/2=1/2sin^-1(4/5)`
If `sin^-1 (2a)/(1+a^2)+sin^-1 (2b)/(1+b^2)=2tan^-1x,` Prove that `x=(a+b)/(1-ab).`
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 cos\[\left( 2 \sin^{- 1} \frac{1}{3} \right)\]
Evaluate sin
\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]
Write the value of cos2 \[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
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
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] is equal to
The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is
If \[3\sin^{- 1} \left( \frac{2x}{1 + x^2} \right) - 4 \cos^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) + 2 \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) = \frac{\pi}{3}\] is equal to
\[\cot\left( \frac{\pi}{4} - 2 \cot^{- 1} 3 \right) =\]
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 value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]
If \[\tan^{- 1} \left( \frac{1}{1 + 1 . 2} \right) + \tan^{- 1} \left( \frac{1}{1 + 2 . 3} \right) + . . . + \tan^{- 1} \left( \frac{1}{1 + n . \left( n + 1 \right)} \right) = \tan^{- 1} \theta\] , then find the value of θ.
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
The value of sin `["cos"^-1 (7/25)]` is ____________.
