Advertisements
Advertisements
Question
Show that xcosecx = `1+x^2/6+(7x^4)/360+......`
Solution
LHS = xcosecx
=` x/sinx`
= `x/(x-x^3/(3!)+x^5/(5!)-x^6/(7!)+..........`
= `x/(x(1- x^2/(3!)+x^4/(5!)-x^6/(7!)+..........)`
=`[(1-(x^2/(3!)-x^4/(5!)+x^6/(7!)))]^(-1)`
=`1+(x^2/(3!)-x^4/(5!)+x^6/(7!)-..........)+(x^2/(3!)-x^4/(5!)+x^6/(7!)-.........)^2+.......{โต(1-y)^1=1+y+y^2+y^3+.............}`
=`1+x^2/3!-x^4/5!+(x^2/3!)+........`
=`1+x^2/6+(7x^4)/360+........`
∴ xcosecx =` 1+x^2/6+(7x^4)/360+........`
APPEARS IN
RELATED QUESTIONS
Show that `sin(e^x-1)=x^1+x^2/2-(5x^4)/24+`...................
Using Newton Raphson method solve 3x – cosx – 1 = 0. Correct upto 3 decimal places.
If y= cos (msin_1 x).Prove that `(1-x^2)y_n+2-(2n+1)xy_(n+1)+(m^2-n^2)y_n=0`
If coshx = secθ prove that (i) x = log(secθ+tanθ). (ii) `θ=pi/2tan^-1(e^-x)`
Prove that `cos^-1tanh(log x)+ = π – 2(x-x^3/3+x^5/5.........)`
If` y= e^2x sin x/2 cos x/2 sin3x. "find" y_n`
Evaluate `Lim _(x→0) (cot x)^sinx.`
Prove that log `[sin(x+iy)/sin(x-iy)]=2tan^-1 (cot x tanhy)`
`"If" sin^4θcos^3θ = acosθ + bcos3θ + ccos5θ + dcos7θ "then find" a,b,c,d.`
Expand sec x by McLaurin’s theorem considering up to x4 term.
