Advertisements
Advertisements
प्रश्न
The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is
विकल्प
`sqrt29/3`
`29/3`
`sqrt3/29`
`3/29`
Advertisements
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
If (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
`sin^-1(sin3)`
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Evaluate the following:
`\text(cosec)^-1(\text{cosec} pi/4)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`cot^-1{cot (-(8pi)/3)}`
Prove the following result
`tan(cos^-1 4/5+tan^-1 2/3)=17/6`
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)`
Find the value of `tan^-1 (x/y)-tan^-1((x-y)/(x+y))`
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`
Solve the following equation for x:
`tan^-1(2+x)+tan^-1(2-x)=tan^-1 2/3, where x< -sqrt3 or, x>sqrt3`
Sum the following series:
`tan^-1 1/3+tan^-1 2/9+tan^-1 4/33+...+tan^-1 (2^(n-1))/(1+2^(2n-1))`
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
`2tan^-1 3/4-tan^-1 17/31=pi/4`
`2tan^-1(1/2)+tan^-1(1/7)=tan^-1(31/17)`
Prove that
`sin{tan^-1 (1-x^2)/(2x)+cos^-1 (1-x^2)/(2x)}=1`
Solve the following equation for x:
`3sin^-1 (2x)/(1+x^2)-4cos^-1 (1-x^2)/(1+x^2)+2tan^-1 (2x)/(1-x^2)=pi/3`
Write the value of cos−1 \[\left( \tan\frac{3\pi}{4} \right)\]
If 4 sin−1 x + cos−1 x = π, then what is the value of x?
Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
Write the value of \[\tan^{- 1} \left( \frac{1}{x} \right)\] for x < 0 in terms of `cot^-1x`
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
If α = \[\tan^{- 1} \left( \frac{\sqrt{3}x}{2y - x} \right), \beta = \tan^{- 1} \left( \frac{2x - y}{\sqrt{3}y} \right),\]
then α − β =
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
\[\tan^{- 1} \left( \frac{a}{b + c} \right) + \tan^{- 1} \left( \frac{b}{c + a} \right) =\]
The value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
Prove that : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
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 period of the function f(x) = tan3x is ____________.
