Advertisements
Advertisements
Question
Wnte the value of\[\cos\left( \frac{\tan^{- 1} x + \cot^{- 1} x}{3} \right), \text{ when } x = - \frac{1}{\sqrt{3}}\]
Solution
\[\cos\left( \frac{\tan^{- 1} x + \cot^{- 1} x}{3} \right) = \cos\left( \frac{\pi}{6} \right) \left[ \because \tan^{- 1} x + \cot^{- 1} x = \frac{\pi}{2} \right]\]
\[ = \frac{\sqrt{3}}{2}\]
APPEARS IN
RELATED QUESTIONS
Solve the following for x:
`sin^(-1)(1-x)-2sin^-1 x=pi/2`
If (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
`sin^-1(sin pi/6)`
`sin^-1(sin (5pi)/6)`
`sin^-1(sin (13pi)/7)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Evaluate the following:
`cot^-1(cot (9pi)/4)`
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)-1)/x},x !=0`
Write the following in the simplest form:
`tan^-1(x/(a+sqrt(a^2-x^2))),-a<x<a`
Evaluate the following:
`sin(cos^-1 5/13)`
Evaluate the following:
`sin(tan^-1 24/7)`
Evaluate the following:
`cosec(cos^-1 3/5)`
Evaluate the following:
`tan(cos^-1 8/17)`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x > 0
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
If `sin^-1x+sin^-1y=pi/3` and `cos^-1x-cos^-1y=pi/6`, find the values of x and y.
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
Solve the following equation for x:
`tan^-1 (x-2)/(x-1)+tan^-1 (x+2)/(x+1)=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`
`2tan^-1 1/5+tan^-1 1/8=tan^-1 4/7`
If `sin^-1 (2a)/(1+a^2)-cos^-1 (1-b^2)/(1+b^2)=tan^-1 (2x)/(1-x^2)`, then prove that `x=(a-b)/(1+ab)`
Write the difference between maximum and minimum values of sin−1 x for x ∈ [− 1, 1].
If tan−1 x + tan−1 y = `pi/4`, then write the value of x + y + xy.
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the value of cos−1 \[\left( \cos\frac{5\pi}{4} \right)\]
Write the value of \[\sin^{- 1} \left( \frac{1}{3} \right) - \cos^{- 1} \left( - \frac{1}{3} \right)\]
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 \[\tan^{- 1} \left( \frac{1}{x} \right)\] for x < 0 in terms of `cot^-1x`
If α = \[\tan^{- 1} \left( \tan\frac{5\pi}{4} \right) \text{ and }\beta = \tan^{- 1} \left( - \tan\frac{2\pi}{3} \right)\] , then
\[\text{ If } u = \cot^{- 1} \sqrt{\tan \theta} - \tan^{- 1} \sqrt{\tan \theta}\text{ then }, \tan\left( \frac{\pi}{4} - \frac{u}{2} \right) =\]
It \[\tan^{- 1} \frac{x + 1}{x - 1} + \tan^{- 1} \frac{x - 1}{x} = \tan^{- 1}\] (−7), then the value of x is
The value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find \[\frac{dy}{dx}\] When \[\theta = \frac{\pi}{3}\] .
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
The period of the function f(x) = tan3x is ____________.
