Advertisements
Advertisements
प्रश्न
Evaluate the following:
`cosec^-1(cosec (11pi)/6)`
Advertisements
उत्तर
We know that
cosec-1 (cosec θ) = θ, [-π/2,0) ∪ (0,π/2]
`cosec^-1(cosec (11pi)/6)=cosec^-1[cosec(2pi-pi/6)]`
`=cosec^-1(cosec - pi/6)`
`=-pi/6`
APPEARS IN
संबंधित प्रश्न
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
Find the principal values of the following:
`cos^-1(tan (3pi)/4)`
`sin^-1{(sin - (17pi)/8)}`
`sin^-1(sin2)`
Evaluate the following:
`tan^-1(tan (6pi)/7)`
Evaluate the following:
`tan^-1(tan (7pi)/6)`
Evaluate the following:
`sec^-1(sec (5pi)/4)`
Write the following in the simplest form:
`tan^-1(x/(a+sqrt(a^2-x^2))),-a<x<a`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Evaluate:
`cos{sin^-1(-7/25)}`
Evaluate:
`cos(tan^-1 3/4)`
If `(sin^-1x)^2+(cos^-1x)^2=(17pi^2)/36,` Find x
`sin^-1x=pi/6+cos^-1x`
Solve the following equation for x:
`tan^-1 2x+tan^-1 3x = npi+(3pi)/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`
Evaluate the following:
`tan{2tan^-1 1/5-pi/4}`
`tan^-1 2/3=1/2tan^-1 12/5`
`2tan^-1 3/4-tan^-1 17/31=pi/4`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
Find the value of the following:
`tan^-1{2cos(2sin^-1 1/2)}`
Solve the following equation for x:
`3sin^-1 (2x)/(1+x^2)-4cos^-1 (1-x^2)/(1+x^2)+2tan^-1 (2x)/(1-x^2)=pi/3`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
If −1 < x < 0, then write the value of `sin^-1((2x)/(1+x^2))+cos^-1((1-x^2)/(1+x^2))`
Write the value of
\[\cos^{- 1} \left( \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\].
If 4 sin−1 x + cos−1 x = π, then what is the value of x?
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
Write the principal value of \[\cos^{- 1} \left( \cos680^\circ \right)\]
Wnte the value of the expression \[\tan\left( \frac{\sin^{- 1} x + \cos^{- 1} x}{2} \right), \text { when } x = \frac{\sqrt{3}}{2}\]
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
Find the value of \[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right)\]
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
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 =
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] is equal to
The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
If x > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
Prove that : \[\cot^{- 1} \frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}} = \frac{x}{2}, 0 < x < \frac{\pi}{2}\] .
