Advertisements
Advertisements
Question
Evaluate the following:
`sin(sec^-1 17/8)`
Solution
`=sin(sec^-1 17/8)=sin(cos^-1 8/17)`
`=sin[sin^-1sqrt(1-(8/17)^2)]` `[thereforecos^-1x=sin^-1sqrt(1-x^2)]`
`=sin[sin^-1(sqrt(1-64/289))]`
`=sin[sin^-1(sqrt(225/289))]`
`=sin[sin^-1 15/17]`
`=15/17`
APPEARS IN
RELATED QUESTIONS
If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy.
Evaluate the following:
`tan^-1(tan pi/3)`
Evaluate the following:
`tan^-1(tan12)`
Evaluate the following:
`sec^-1{sec (-(7pi)/3)}`
Evaluate the following:
`cot^-1(cot (19pi)/6)`
Write the following in the simplest form:
`cot^-1 a/sqrt(x^2-a^2),| x | > a`
Write the following in the simplest form:
`tan^-1{sqrt(1+x^2)-x},x in R `
Evaluate the following:
`sec(sin^-1 12/13)`
Evaluate the following:
`cot(cos^-1 3/5)`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Prove the following result-
`tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x < 0
`5tan^-1x+3cot^-1x=2x`
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
Solve the following equation for x:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
Solve the following equation for x:
tan−1(x + 2) + tan−1(x − 2) = tan−1 `(8/79)`, x > 0
Solve the following equation for x:
`tan^-1((x-2)/(x-4))+tan^-1((x+2)/(x+4))=pi/4`
If `cos^-1 x/2+cos^-1 y/3=alpha,` then prove that `9x^2-12xy cosa+4y^2=36sin^2a.`
Solve `cos^-1sqrt3x+cos^-1x=pi/2`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
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`
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.
What is the value of cos−1 `(cos (2x)/3)+sin^-1(sin (2x)/3)?`
Evaluate sin
\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]
Write the value of cos2 \[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]
Write the value of \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
Wnte the value of\[\cos\left( \frac{\tan^{- 1} x + \cot^{- 1} x}{3} \right), \text{ when } x = - \frac{1}{\sqrt{3}}\]
The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is
If \[\cos^{- 1} \frac{x}{a} + \cos^{- 1} \frac{y}{b} = \alpha, then\frac{x^2}{a^2} - \frac{2xy}{ab}\cos \alpha + \frac{y^2}{b^2} = \]
The number of real solutions of the equation \[\sqrt{1 + \cos 2x} = \sqrt{2} \sin^{- 1} (\sin x), - \pi \leq x \leq \pi\]
The value of \[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right)\] is
sin \[\left\{ 2 \cos^{- 1} \left( \frac{- 3}{5} \right) \right\}\] is equal to
It \[\tan^{- 1} \frac{x + 1}{x - 1} + \tan^{- 1} \frac{x - 1}{x} = \tan^{- 1}\] (−7), then the value of x is
If tan−1 (cot θ) = 2 θ, then θ =
The value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]
Solve for x : {xcos(cot-1 x) + sin(cot-1 x)}2 = `51/50`
