Advertisements
Advertisements
Question
If \[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\] , find the value of x.
Solution
\[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\]
\[ \Rightarrow \cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = \cos\left( \frac{\pi}{2} \right)\]
\[ \Rightarrow \tan^{- 1} x + \cot^{- 1} \sqrt{3} = \frac{\pi}{2}\]
\[ \Rightarrow x = \sqrt{3} \left[ \because \tan^{- 1} y + \cot^{- 1} y = \frac{\pi}{2} \right]\]
\[\]
APPEARS IN
RELATED QUESTIONS
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
Find the principal values of the following:
`cos^-1(-1/sqrt2)`
Evaluate the following:
`tan^-1(tan (6pi)/7)`
Evaluate the following:
`cosec^-1(cosec (3pi)/4)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`cosec^-1(cosec (11pi)/6)`
Write the following in the simplest form:
`tan^-1(x/(a+sqrt(a^2-x^2))),-a<x<a`
Solve: `cos(sin^-1x)=1/6`
Evaluate:
`tan{cos^-1(-7/25)}`
If `cot(cos^-1 3/5+sin^-1x)=0`, find the values of x.
`sin(sin^-1 1/5+cos^-1x)=1`
Solve the following equation for x:
tan−1`((1-x)/(1+x))-1/2` tan−1x = 0, where x > 0
Solve the following equation for x:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
Solve the following equation for x:
`tan^-1((x-2)/(x-4))+tan^-1((x+2)/(x+4))=pi/4`
`sin^-1 63/65=sin^-1 5/13+cos^-1 3/5`
Evaluate the following:
`tan 1/2(cos^-1 sqrt5/3)`
Evaluate the following:
`sin(2tan^-1 2/3)+cos(tan^-1sqrt3)`
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
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 sin−1 (sin 1550°).
Evaluate sin \[\left( \tan^{- 1} \frac{3}{4} \right)\]
Write the value of \[\sin^{- 1} \left( \frac{1}{3} \right) - \cos^{- 1} \left( - \frac{1}{3} \right)\]
Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`
If \[\cos^{- 1} \frac{x}{a} + \cos^{- 1} \frac{y}{b} = \alpha, then\frac{x^2}{a^2} - \frac{2xy}{ab}\cos \alpha + \frac{y^2}{b^2} = \]
Let f (x) = `e^(cos^-1){sin(x+pi/3}.`
Then, f (8π/9) =
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
\[\tan^{- 1} \left( \frac{a}{b + c} \right) + \tan^{- 1} \left( \frac{b}{c + a} \right) =\]
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find \[\frac{dy}{dx}\] When \[\theta = \frac{\pi}{3}\] .
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
