Advertisements
Advertisements
प्रश्न
Evaluate the following:
`cot^-1(cot (4pi)/3)`
उत्तर
We know that
cot-1 (cot θ) = θ, (0, π)
We have
`cot^-1(cot (4pi)/3)=cot^-1[cot(pi+pi/3)]`
`=cot^-1(cot pi/3)`
`=pi/3`
APPEARS IN
संबंधित प्रश्न
Find the value of the following: `tan(1/2)[sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))],|x| <1,y>0 and xy <1`
Find the principal values of the following:
`cos^-1(tan (3pi)/4)`
`sin^-1(sin (7pi)/6)`
`sin^-1(sin3)`
Evaluate the following:
`tan^-1(tan4)`
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^-1sqrt((a-x)/(a+x)),-a<x<a`
Evaluate the following:
`sin(sin^-1 7/25)`
Evaluate the following:
`sin(sec^-1 17/8)`
Evaluate the following:
`cosec(cos^-1 3/5)`
Evaluate the following:
`sec(sin^-1 12/13)`
Solve: `cos(sin^-1x)=1/6`
Evaluate:
`cos{sin^-1(-7/25)}`
Evaluate:
`cot{sec^-1(-13/5)}`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x > 0
`sin^-1x=pi/6+cos^-1x`
`tan^-1x+2cot^-1x=(2x)/3`
`5tan^-1x+3cot^-1x=2x`
Prove the following result:
`tan^-1 1/4+tan^-1 2/9=sin^-1 1/sqrt5`
Find the value of `tan^-1 (x/y)-tan^-1((x-y)/(x+y))`
Solve the following equation for x:
`tan^-1 2x+tan^-1 3x = npi+(3pi)/4`
Solve the following equation for x:
tan−1(x + 1) + tan−1(x − 1) = tan−1`8/31`
Solve the following equation for x:
tan−1(x −1) + tan−1x tan−1(x + 1) = tan−13x
If `cos^-1 x/2+cos^-1 y/3=alpha,` then prove that `9x^2-12xy cosa+4y^2=36sin^2a.`
`2sin^-1 3/5-tan^-1 17/31=pi/4`
Show that `2tan^-1x+sin^-1 (2x)/(1+x^2)` is constant for x ≥ 1, find that constant.
Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
Write the difference between maximum and minimum values of sin−1 x for x ∈ [− 1, 1].
Write the value of sin (cot−1 x).
Write the value of \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]
Show that \[\sin^{- 1} (2x\sqrt{1 - x^2}) = 2 \sin^{- 1} x\]
Find the value of \[2 \sec^{- 1} 2 + \sin^{- 1} \left( \frac{1}{2} \right)\]
sin\[\left[ \cot^{- 1} \left\{ \tan\left( \cos^{- 1} x \right) \right\} \right]\] is equal to
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
If y = sin (sin x), prove that \[\frac{d^2 y}{d x^2} + \tan x \frac{dy}{dx} + y \cos^2 x = 0 .\]
Prove that : \[\cot^{- 1} \frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}} = \frac{x}{2}, 0 < x < \frac{\pi}{2}\] .
Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
