Advertisements
Advertisements
Question
Evaluate the following:
`cosec^-1{cosec (-(9pi)/4)}`
Advertisements
Solution
We know that
cosec-1 (cosec θ) = θ, [-π/2,0) ∪ (0,π/2]
`cosec^-1{cosec (-(9pi)/4)}=cosec^-1[-cosec(2pi+pi/4)]`
`=cosec^-1(-cosec pi/4)`
`=cosec^-1(cosec-pi/4)`
`=-pi/4`
APPEARS IN
RELATED QUESTIONS
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
`sin^-1(sin pi/6)`
`sin^-1(sin3)`
Evaluate the following:
`tan^-1(tan pi/3)`
Evaluate the following:
`sec^-1(sec (25pi)/6)`
Evaluate the following:
`\text(cosec)^-1(\text{cosec} pi/4)`
Evaluate the following:
`cot^-1(cot (4pi)/3)`
Evaluate the following:
`cosec(cos^-1 3/5)`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x < 0
Solve the following equation for x:
tan−1(x + 1) + tan−1(x − 1) = tan−1`8/31`
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))`
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
If `cos^-1 x/2+cos^-1 y/3=alpha,` then prove that `9x^2-12xy cosa+4y^2=36sin^2a.`
Prove that:
`2sin^-1 3/5=tan^-1 24/7`
`sin^-1 4/5+2tan^-1 1/3=pi/2`
Solve the following equation for x:
`2tan^-1(sinx)=tan^-1(2sinx),x!=pi/2`
Solve the following equation for x:
`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`
Solve the following equation for x:
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.
Write the value of tan−1 x + tan−1 `(1/x)` for x < 0.
Write the value of sin (cot−1 x).
Write the value of cos−1 (cos 1540°).
Write the value of cos−1 (cos 6).
If 4 sin−1 x + cos−1 x = π, then what is the value of x?
Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`
Write the value of \[\tan^{- 1} \left( \frac{1}{x} \right)\] for x < 0 in terms of `cot^-1x`
The number of real solutions of the equation \[\sqrt{1 + \cos 2x} = \sqrt{2} \sin^{- 1} (\sin x), - \pi \leq x \leq \pi\]
If α = \[\tan^{- 1} \left( \frac{\sqrt{3}x}{2y - x} \right), \beta = \tan^{- 1} \left( \frac{2x - y}{\sqrt{3}y} \right),\]
then α − β =
If \[\sin^{- 1} \left( \frac{2a}{1 - a^2} \right) + \cos^{- 1} \left( \frac{1 - a^2}{1 + a^2} \right) = \tan^{- 1} \left( \frac{2x}{1 - x^2} \right),\text{ where }a, x \in \left( 0, 1 \right)\] , then, the value of x is
Prove that : \[\cot^{- 1} \frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}} = \frac{x}{2}, 0 < x < \frac{\pi}{2}\] .
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.
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
The value of sin `["cos"^-1 (7/25)]` is ____________.
The value of tan `("cos"^-1 4/5 + "tan"^-1 2/3) =`
