Advertisements
Advertisements
प्रश्न
Evaluate the following:
`sec^-1(sec (5pi)/4)`
Advertisements
उत्तर
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
संबंधित प्रश्न
Write the value of `tan(2tan^(-1)(1/5))`
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
`sin^-1(sin pi/6)`
`sin^-1(sin (5pi)/6)`
Evaluate the following:
`cos^-1{cos ((4pi)/3)}`
Evaluate the following:
`tan^-1(tan (9pi)/4)`
Evaluate the following:
`tan^-1(tan1)`
Evaluate the following:
`tan^-1(tan4)`
Evaluate the following:
`sec^-1(sec (7pi)/3)`
Evaluate the following:
`cot(cos^-1 3/5)`
Evaluate:
`cos{sin^-1(-7/25)}`
Evaluate:
`sec{cot^-1(-5/12)}`
Evaluate:
`tan{cos^-1(-7/25)}`
Evaluate:
`cot(tan^-1a+cot^-1a)`
`sin^-1x=pi/6+cos^-1x`
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
Solve the following equation for x:
`tan^-1 (x-2)/(x-1)+tan^-1 (x+2)/(x+1)=pi/4`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
If `cos^-1 x/2+cos^-1 y/3=alpha,` then prove that `9x^2-12xy cosa+4y^2=36sin^2a.`
`2tan^-1 3/4-tan^-1 17/31=pi/4`
Solve the following equation for x:
`2tan^-1(sinx)=tan^-1(2sinx),x!=pi/2`
Prove that:
`tan^-1 (2ab)/(a^2-b^2)+tan^-1 (2xy)/(x^2-y^2)=tan^-1 (2alphabeta)/(alpha^2-beta^2),` where `alpha=ax-by and beta=ay+bx.`
If `sin^-1x+sin^-1y+sin^-1z=(3pi)/2,` then write the value of x + y + z.
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
Write the value of cos−1 \[\left( \cos\frac{5\pi}{4} \right)\]
If \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find x.
Write the principal value of \[\cos^{- 1} \left( \cos\frac{2\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{2\pi}{3} \right)\]
Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is
The domain of \[\cos^{- 1} \left( x^2 - 4 \right)\] is
Prove that : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
Find the domain of `sec^(-1)(3x-1)`.
