Advertisements
Advertisements
प्रश्न
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
Advertisements
उत्तर
We have
\[\tan^{- 1} \left\{ \tan\left( \frac{15\pi}{4} \right) \right\} = \tan^{- 1} \left\{ \tan\left( 4\pi - \frac{\pi}{4} \right) \right\}\]
\[ \tan^{- 1} \left\{ - \tan\left( \frac{\pi}{4} \right) \right\} \left[ \because \tan\left( 4\pi - x \right) = - \tan{x} \right]\]
\[ = \tan^{- 1} \left\{ \tan\left( - \frac{\pi}{4} \right) \right\} \]
\[ = - \frac{\pi}{4} \left[ \because \tan^{- 1} \left( \tan{x} \right) = x \right] \]
∴ \[\tan^{- 1} \left\{ \tan\left( \frac{15\pi}{4} \right) \right\} = - \frac{\pi}{4}\]
APPEARS IN
संबंधित प्रश्न
Write the value of `tan(2tan^(-1)(1/5))`
Solve the equation for x:sin−1x+sin−1(1−x)=cos−1x
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`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
Prove that
`tan^(-1) [(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))]=pi/4-1/2 cos^(-1)x,-1/sqrt2<=x<=1`
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.
`sin^-1(sin pi/6)`
`sin^-1(sin (13pi)/7)`
`sin^-1(sin (17pi)/8)`
`sin^-1(sin4)`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`cos^-1(cos3)`
Evaluate the following:
`sec^-1(sec (25pi)/6)`
Evaluate the following:
`cot^-1(cot (19pi)/6)`
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)-1)/x},x !=0`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Evaluate the following:
`sin(sec^-1 17/8)`
Evaluate:
`cot(tan^-1a+cot^-1a)`
If `sin^-1x+sin^-1y=pi/3` and `cos^-1x-cos^-1y=pi/6`, find the values of x and y.
`sin(sin^-1 1/5+cos^-1x)=1`
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
Solve the following equation for x:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
If `cos^-1 x/2+cos^-1 y/3=alpha,` then prove that `9x^2-12xy cosa+4y^2=36sin^2a.`
Solve `cos^-1sqrt3x+cos^-1x=pi/2`
`tan^-1 2/3=1/2tan^-1 12/5`
Solve the following equation for x:
`tan^-1 1/4+2tan^-1 1/5+tan^-1 1/6+tan^-1 1/x=pi/4`
Write the value of sin−1
\[\left( \sin( -{600}°) \right)\].
Evaluate sin \[\left( \tan^{- 1} \frac{3}{4} \right)\]
Show that \[\sin^{- 1} (2x\sqrt{1 - x^2}) = 2 \sin^{- 1} x\]
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
Find the value of \[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right)\]
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
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
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find \[\frac{dy}{dx}\] When \[\theta = \frac{\pi}{3}\] .
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.
Write the value of \[\cos^{- 1} \left( - \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\] .
Find the domain of `sec^(-1) x-tan^(-1)x`
