Advertisements
Advertisements
प्रश्न
Evaluate:
`cosec{cot^-1(-12/5)}`
Advertisements
उत्तर
`cosec{cot^-1(-12/5)}=cosec{cot^-1(pi-12/5)}`
`=cosec{cot^-1(12/5)}`
`=cosec{sin^-1((5/12)/sqrt(1+(5/12)^2))}`
`=cosec{sin^-1(5/13)}`
`=cosec{cosec^-1(13/5)}`
`=13/5`
APPEARS IN
संबंधित प्रश्न
Prove that :
`2 tan^-1 (sqrt((a-b)/(a+b))tan(x/2))=cos^-1 ((a cos x+b)/(a+b cosx))`
If `(sin^-1x)^2 + (sin^-1y)^2+(sin^-1z)^2=3/4pi^2,` find the value of x2 + y2 + z2
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
`sin^-1(sin (13pi)/7)`
`sin^-1{(sin - (17pi)/8)}`
Evaluate the following:
`tan^-1(tan2)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`cosec^-1(cosec (11pi)/6)`
Evaluate the following:
`cosec^-1(cosec (13pi)/6)`
Evaluate the following:
`cot^-1(cot (9pi)/4)`
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{2tan^-1sqrt((1-x)/(1+x))}`
Evaluate:
`cot(tan^-1a+cot^-1a)`
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
`4sin^-1x=pi-cos^-1x`
Solve the following equation for x:
`tan^-1((x-2)/(x-4))+tan^-1((x+2)/(x+4))=pi/4`
Solve the following equation for x:
`tan^-1(2+x)+tan^-1(2-x)=tan^-1 2/3, where x< -sqrt3 or, x>sqrt3`
If `cos^-1 x/2+cos^-1 y/3=alpha,` then prove that `9x^2-12xy cosa+4y^2=36sin^2a.`
Evaluate the following:
`sin(1/2cos^-1 4/5)`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=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.`
Write the value of tan−1 x + tan−1 `(1/x)` for x < 0.
Write the value of sin (cot−1 x).
If tan−1 x + tan−1 y = `pi/4`, then write the value of x + y + xy.
Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
If \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} - \sqrt{1 - x^2}}{\sqrt{1 + x^2} + \sqrt{1 - x^2}} \right)\] = α, then x2 =
The positive integral solution of the equation
\[\tan^{- 1} x + \cos^{- 1} \frac{y}{\sqrt{1 + y^2}} = \sin^{- 1} \frac{3}{\sqrt{10}}\text{ is }\]
If α = \[\tan^{- 1} \left( \tan\frac{5\pi}{4} \right) \text{ and }\beta = \tan^{- 1} \left( - \tan\frac{2\pi}{3} \right)\] , then
If tan−1 3 + tan−1 x = tan−1 8, then x =
If tan−1 (cot θ) = 2 θ, then θ =
If 2 tan−1 (cos θ) = tan−1 (2 cosec θ), (θ ≠ 0), then find the value of θ.
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.
Write the value of \[\cos^{- 1} \left( - \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\] .
Find the value of `sin^-1(cos((33π)/5))`.
