Advertisements
Advertisements
Question
Evaluate:
`cosec{cot^-1(-12/5)}`
Advertisements
Solution
`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
RELATED QUESTIONS
Solve the equation for x:sin−1x+sin−1(1−x)=cos−1x
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Evaluate the following:
`cos^-1(cos4)`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`sec^-1(sec (7pi)/3)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Evaluate the following:
`sec^-1(sec (25pi)/6)`
Evaluate the following:
`cot^-1(cot pi/3)`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Evaluate the following:
`tan(cos^-1 8/17)`
Evaluate:
`cot{sec^-1(-13/5)}`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
`4sin^-1x=pi-cos^-1x`
Solve the following equation for x:
tan−1(x + 2) + tan−1(x − 2) = tan−1 `(8/79)`, x > 0
Solve `cos^-1sqrt3x+cos^-1x=pi/2`
`tan^-1 1/4+tan^-1 2/9=1/2cos^-1 3/2=1/2sin^-1(4/5)`
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=pi/2`
Prove that
`sin{tan^-1 (1-x^2)/(2x)+cos^-1 (1-x^2)/(2x)}=1`
Find the value of the following:
`tan^-1{2cos(2sin^-1 1/2)}`
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 `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
Write the value of \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]
If \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find x.
Write the value of \[\sin^{- 1} \left( \frac{1}{3} \right) - \cos^{- 1} \left( - \frac{1}{3} \right)\]
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 value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] 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
Let f (x) = `e^(cos^-1){sin(x+pi/3}.`
Then, f (8π/9) =
If tan−1 3 + tan−1 x = tan−1 8, then x =
The value of \[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right)\] is
The value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]
Write the value of \[\cos^{- 1} \left( - \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\] .
Solve for x : {xcos(cot-1 x) + sin(cot-1 x)}2 = `51/50`
