Advertisements
Advertisements
Question
Evaluate the following:
`tan(cos^-1 8/17)`
Advertisements
Solution
`tan(cos^-1 8/17)=tan{tan^-1 (sqrt(1-(8/17)^2))/(8/17)}` `[thereforecos^-1x=tan^-1 ((sqrt(1-x^2))/x)]`
`=tan(tan^-1 (15/17)/(8/17))`
`=15/8`
APPEARS IN
RELATED QUESTIONS
Write the value of `tan(2tan^(-1)(1/5))`
If `cos^-1( x/a) +cos^-1 (y/b)=alpha` , prove that `x^2/a^2-2(xy)/(ab) cos alpha +y^2/b^2=sin^2alpha`
If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy.
If `(sin^-1x)^2 + (sin^-1y)^2+(sin^-1z)^2=3/4pi^2,` find the value of x2 + y2 + z2
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
Evaluate the following:
`tan^-1(tan (7pi)/6)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`cot^-1{cot ((21pi)/4)}`
Write the following in the simplest form:
`tan^-1{x+sqrt(1+x^2)},x in R `
Write the following in the simplest form:
`tan^-1{sqrt(1+x^2)-x},x in R`
Write the following in the simplest form:
`sin^-1{(sqrt(1+x)+sqrt(1-x))/2},0<x<1`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Evaluate the following:
`sin(tan^-1 24/7)`
Evaluate the following:
`sin(sec^-1 17/8)`
Prove the following result-
`tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5`
Evaluate:
`sec{cot^-1(-5/12)}`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
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
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
What is the value of cos−1 `(cos (2x)/3)+sin^-1(sin (2x)/3)?`
Write the value of
\[\cos^{- 1} \left( \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\].
Write the value of cos−1 (cos 1540°).
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
Write the value of \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]
The set of values of `\text(cosec)^-1(sqrt3/2)`
Write the value of \[\tan^{- 1} \left( \frac{1}{x} \right)\] for x < 0 in terms of `cot^-1x`
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
If \[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\] , find the value of x.
The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] is
If tan−1 (cot θ) = 2 θ, then θ =
If x > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find \[\frac{dy}{dx}\] When \[\theta = \frac{\pi}{3}\] .
