Advertisements
Advertisements
Question
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Solution
We know that
sec-1 (sec θ) = θ, [0, π/2) ∪ (π/2, π]
We have
`sec^-1(sec (2pi)/3)=(2pi)/3`
APPEARS IN
RELATED QUESTIONS
Write the value of `tan(2tan^(-1)(1/5))`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
`sin^-1{(sin - (17pi)/8)}`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Evaluate the following:
`cosec^-1(cosec (13pi)/6)`
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`
Write the following in the simplest form:
`sin^-1{(sqrt(1+x)+sqrt(1-x))/2},0<x<1`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Evaluate:
`cosec{cot^-1(-12/5)}`
Evaluate:
`cos(sec^-1x+\text(cosec)^-1x)`,|x|≥1
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
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:
`tan^-1 (x-2)/(x-1)+tan^-1 (x+2)/(x+1)=pi/4`
Solve `cos^-1sqrt3x+cos^-1x=pi/2`
Evaluate the following:
`tan 1/2(cos^-1 sqrt5/3)`
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=pi/2`
Show that `2tan^-1x+sin^-1 (2x)/(1+x^2)` is constant for x ≥ 1, find that constant.
Write the value of cos−1 (cos 1540°).
Write the value of cos2 \[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]
If \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find x.
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the value of \[\sec^{- 1} \left( \frac{1}{2} \right)\]
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 principal value of \[\sin^{- 1} \left\{ \cos\left( \sin^{- 1} \frac{1}{2} \right) \right\}\]
Write the value of \[\tan^{- 1} \left( \frac{1}{x} \right)\] for x < 0 in terms of `cot^-1x`
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
Find the value of \[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right)\]
sin\[\left[ \cot^{- 1} \left\{ \tan\left( \cos^{- 1} x \right) \right\} \right]\] is equal to
If α = \[\tan^{- 1} \left( \tan\frac{5\pi}{4} \right) \text{ and }\beta = \tan^{- 1} \left( - \tan\frac{2\pi}{3} \right)\] , then
Let f (x) = `e^(cos^-1){sin(x+pi/3}.`
Then, f (8π/9) =
If \[\cos^{- 1} \frac{x}{2} + \cos^{- 1} \frac{y}{3} = \theta,\] then 9x2 − 12xy cos θ + 4y2 is equal to
sin \[\left\{ 2 \cos^{- 1} \left( \frac{- 3}{5} \right) \right\}\] is equal to
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 \[\tan^{- 1} \left( \frac{1}{1 + 1 . 2} \right) + \tan^{- 1} \left( \frac{1}{1 + 2 . 3} \right) + . . . + \tan^{- 1} \left( \frac{1}{1 + n . \left( n + 1 \right)} \right) = \tan^{- 1} \theta\] , then find the value of θ.
The value of tan `("cos"^-1 4/5 + "tan"^-1 2/3) =`