Advertisements
Advertisements
प्रश्न
The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is
पर्याय
`sqrt29/3`
`29/3`
`sqrt3/29`
`3/29`
उत्तर
(d) `3/29`
\[\text{ Let }, \cos^{- 1} \frac{1}{5\sqrt{2}} = y \text{ and } \sin^{- 1} \frac{4}{\sqrt{17}} = z\]
\[\therefore \cos{y} = \frac{1}{5\sqrt{2}} \Rightarrow \sin{y} = \frac{7}{5\sqrt{2}} \Rightarrow \tan{y} = 7\]
\[\sin{z} = \frac{4}{\sqrt{17}} \Rightarrow \cos{z} = \frac{1}{\sqrt{17}} \Rightarrow \tan{z} = 4\]
\[\therefore \tan\left( \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right) = \tan\left( y - z \right)\]
\[ = \frac{\tan{y} - \tan{z}}{1 + \tan{y} \tan{z}}\]
\[ = \frac{7 - 4}{1 + 7 \times 4}\]
\[ = \frac{3}{29}\]
\[\therefore \tan\left( \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right) = \tan\left( y - z \right)\]
\[ = \frac{\tan{y} - \tan{z}}1 + \tan{y} \tan{z}\]
\[ = \frac{7 - 4}{1 + 7 \times 4}\]
\[ = \frac{3}{29}\]
APPEARS IN
संबंधित प्रश्न
Find the value of the following: `tan(1/2)[sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))],|x| <1,y>0 and xy <1`
Solve the equation for x:sin−1x+sin−1(1−x)=cos−1x
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
`sin^-1(sin4)`
Evaluate the following:
`cos^-1(cos4)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`tan^-1(tan4)`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`sec(sin^-1 12/13)`
Prove the following result-
`tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
`sin^-1x=pi/6+cos^-1x`
Solve the following equation for x:
`tan^-1 2x+tan^-1 3x = npi+(3pi)/4`
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`
`(9pi)/8-9/4sin^-1 1/3=9/4sin^-1 (2sqrt2)/3`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
`tan^-1 1/7+2tan^-1 1/3=pi/4`
`2tan^-1 1/5+tan^-1 1/8=tan^-1 4/7`
If `sin^-1 (2a)/(1+a^2)+sin^-1 (2b)/(1+b^2)=2tan^-1x,` Prove that `x=(a+b)/(1-ab).`
Solve the following equation for x:
`tan^-1 1/4+2tan^-1 1/5+tan^-1 1/6+tan^-1 1/x=pi/4`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.
What is the value of cos−1 `(cos (2x)/3)+sin^-1(sin (2x)/3)?`
Write the range of tan−1 x.
Write the value of cos2 \[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]
Write the value of sin−1 \[\left( \cos\frac{\pi}{9} \right)\]
Show that \[\sin^{- 1} (2x\sqrt{1 - x^2}) = 2 \sin^{- 1} x\]
Wnte the value of the expression \[\tan\left( \frac{\sin^{- 1} x + \cos^{- 1} x}{2} \right), \text { when } x = \frac{\sqrt{3}}{2}\]
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
If tan−1 3 + tan−1 x = tan−1 8, then x =
The value of \[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right)\] is
In a ∆ ABC, if C is a right angle, then
\[\tan^{- 1} \left( \frac{a}{b + c} \right) + \tan^{- 1} \left( \frac{b}{c + a} \right) =\]
Prove that : \[\cot^{- 1} \frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}} = \frac{x}{2}, 0 < x < \frac{\pi}{2}\] .
The equation sin-1 x – cos-1 x = cos-1 `(sqrt3/2)` has ____________.
