Advertisements
Advertisements
Question
Prove that `log(secx)=1/2x^2+1/12x^4+.........`
Sum
Solution
Let E = log (sec x)
= - log (cos x)
`=-log[1-(x^2/(2!)-x^4/(4!))]`
`=-[-(x^2/(2!)-x^4/(4!))-1/2(x^2/(2!)-x^4/(4!))+........]`
E = `log(secx)=1/2x^2+1/12x^4+.........`
shaalaa.com
Logarithmic Functions
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
Prove that log `[tan(pi/4+(ix)/2)]=i.tan^-1(sinhx)`
If `Z=x^2 tan-1y /x-y^2 tan -1 x/y del`
Prove that `(del^z z)/(del_ydel_x)=(x^2-y^2)/(x^2+y^2)`
Show that `ilog((x-i)/(x+i))=pi-2tan6-1x`
Show that sec h-1(sin θ) =log cot (`theta/2` ).
If y = log `[tan(pi/4+x/2)]`Prove that
I. tan h`y/2 = tan pi/2`
II. cos hy cos x = 1
