Advertisements
Advertisements
Question
Evaluate the following:
`sec^-1(sec (5pi)/4)`
Advertisements
Solution
We know that
sec-1 (sec θ) = θ, [0, π/2) ∪ (π/2, π]
We have
`sec^-1(sec (5pi)/4)=sec^-1[sec(2pi-(3pi)/4)]`
`=sec^-1[sec((3pi)/4)]`
`=(3pi)/4`
APPEARS IN
RELATED QUESTIONS
Write the value of `tan(2tan^(-1)(1/5))`
`sin^-1(sin pi/6)`
`sin^-1(sin4)`
`sin^-1(sin2)`
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Evaluate the following:
`tan^-1(tan (7pi)/6)`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`\text(cosec)^-1(\text{cosec} pi/4)`
Write the following in the simplest form:
`sin^-1{(sqrt(1+x)+sqrt(1-x))/2},0<x<1`
Evaluate:
`sec{cot^-1(-5/12)}`
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
If `(sin^-1x)^2+(cos^-1x)^2=(17pi^2)/36,` Find x
Find the value of `tan^-1 (x/y)-tan^-1((x-y)/(x+y))`
Solve the following equation for x:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
Sum the following series:
`tan^-1 1/3+tan^-1 2/9+tan^-1 4/33+...+tan^-1 (2^(n-1))/(1+2^(2n-1))`
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
`tan^-1 1/4+tan^-1 2/9=1/2cos^-1 3/2=1/2sin^-1(4/5)`
Find the value of the following:
`tan^-1{2cos(2sin^-1 1/2)}`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
What is the value of cos−1 `(cos (2x)/3)+sin^-1(sin (2x)/3)?`
Evaluate sin
\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]
Show that \[\sin^{- 1} (2x\sqrt{1 - x^2}) = 2 \sin^{- 1} x\]
If \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find x.
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the principal value of \[\cos^{- 1} \left( \cos680^\circ \right)\]
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
Find the value of \[2 \sec^{- 1} 2 + \sin^{- 1} \left( \frac{1}{2} \right)\]
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
Find the value of \[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right)\]
If sin−1 x − cos−1 x = `pi/6` , then x =
If \[\cos^{- 1} \frac{x}{2} + \cos^{- 1} \frac{y}{3} = \theta,\] then 9x2 − 12xy cos θ + 4y2 is equal to
If 4 cos−1 x + sin−1 x = π, then the value of x is
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
If x > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
Find the domain of `sec^(-1)(3x-1)`.
Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
The period of the function f(x) = tan3x is ____________.
