Advertisements
Advertisements
प्रश्न
If tan−1 (cot θ) = 2 θ, then θ =
पर्याय
`+-pi/3`
`+-pi/4`
`+-pi/6`
none of these
उत्तर
(c) `+-pi/6`
\[\text{We have}, \]
\[ \tan^{- 1} \left( cot\theta \right) = 2\theta\]
\[ \Rightarrow \tan2\theta = cot\theta\]
\[ \Rightarrow \frac{2\tan\theta}{1 - \tan^2 \theta} = \frac{1}{\tan\theta}\]
\[ \Rightarrow 2 \tan^2 \theta = 1 - \tan^2 \theta\]
\[ \Rightarrow 3 \tan^2 \theta = 1\]
\[ \Rightarrow \tan^2 \theta = \frac{1}{3}\]
\[ \Rightarrow \tan\theta = \pm \frac{1}{\sqrt{3}}\]
\[ \therefore \theta = \pm \frac{\pi}{6}\]
APPEARS IN
संबंधित प्रश्न
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
If (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
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.`
`sin^-1(sin (5pi)/6)`
`sin^-1(sin (13pi)/7)`
`sin^-1{(sin - (17pi)/8)}`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Evaluate the following:
`tan^-1(tan (9pi)/4)`
Evaluate the following:
`sec^-1(sec (25pi)/6)`
Evaluate the following:
`cosec^-1(cosec (11pi)/6)`
Evaluate the following:
`cot^-1(cot (19pi)/6)`
Evaluate the following:
`cot^-1{cot (-(8pi)/3)}`
Write the following in the simplest form:
`tan^-1{sqrt(1+x^2)-x},x in R `
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)+1)/x},x !=0`
Evaluate the following:
`sin(sin^-1 7/25)`
Prove the following result
`tan(cos^-1 4/5+tan^-1 2/3)=17/6`
Evaluate:
`cos(tan^-1 3/4)`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x < 0
Evaluate:
`cos(sec^-1x+\text(cosec)^-1x)`,|x|≥1
Solve the following equation for x:
tan−1(x + 1) + tan−1(x − 1) = tan−1`8/31`
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
Show that `2tan^-1x+sin^-1 (2x)/(1+x^2)` is constant for x ≥ 1, find that constant.
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
If tan−1 x + tan−1 y = `pi/4`, then write the value of x + y + xy.
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
If \[\sin^{- 1} \left( \frac{1}{3} \right) + \cos^{- 1} x = \frac{\pi}{2},\] then find x.
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`
If \[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\] , find the value of x.
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is
If θ = sin−1 {sin (−600°)}, then one of the possible values of θ is
It \[\tan^{- 1} \frac{x + 1}{x - 1} + \tan^{- 1} \frac{x - 1}{x} = \tan^{- 1}\] (−7), then the value of x is
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
