Advertisements
Advertisements
प्रश्न
Find the value of the following:
`cos(sec^-1x+\text(cosec)^-1x),` | x | ≥ 1
उत्तर
We have
`cos(sec^-1x+\text(cosec)^-1x)`
`=cos pi/2` `[becausesec^-1x+\text(cosec)^-1x=pi/2]`
= 0
`thereforecos(sec^-1x+\text(cosec)^-1x)=0` , ∣ x ∣ ≥1
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`
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
Find the principal values of the following:
`cos^-1(tan (3pi)/4)`
`sin^-1{(sin - (17pi)/8)}`
`sin^-1(sin12)`
Evaluate the following:
`cos^-1(cos3)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`tan^-1(tan1)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Evaluate the following:
`cosec^-1{cosec (-(9pi)/4)}`
Evaluate the following:
`cot^-1(cot pi/3)`
Evaluate the following:
`cot^-1(cot (9pi)/4)`
Evaluate the following:
`cot^-1{cot ((21pi)/4)}`
Write the following in the simplest form:
`cot^-1 a/sqrt(x^2-a^2),| x | > a`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`
`5tan^-1x+3cot^-1x=2x`
Solve the following equation for x:
tan−1`((1-x)/(1+x))-1/2` tan−1x = 0, where x > 0
Evaluate the following:
`sin(1/2cos^-1 4/5)`
`tan^-1 1/4+tan^-1 2/9=1/2cos^-1 3/2=1/2sin^-1(4/5)`
`2tan^-1(1/2)+tan^-1(1/7)=tan^-1(31/17)`
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=pi/2`
If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.
Write the value of sin (cot−1 x).
Evaluate sin
\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]
Write the value of sin−1 \[\left( \cos\frac{\pi}{9} \right)\]
Write the value of sin \[\left\{ \frac{\pi}{3} - \sin^{- 1} \left( - \frac{1}{2} \right) \right\}\]
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
The set of values of `\text(cosec)^-1(sqrt3/2)`
Find the value of \[2 \sec^{- 1} 2 + \sin^{- 1} \left( \frac{1}{2} \right)\]
sin \[\left\{ 2 \cos^{- 1} \left( \frac{- 3}{5} \right) \right\}\] is equal to
If 4 cos−1 x + sin−1 x = π, then the value of x is
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 : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
tanx is periodic with period ____________.
Solve for x : {xcos(cot-1 x) + sin(cot-1 x)}2 = `51/50`
