Question

X sin a - a sin x by x -a

Answer 1

it is the qn of limits in calculus.

$Ans= \lim_{x \to a}\ \frac{x\ sin a-a\ sin x}{x-a}\\\\let\ x-a=h,\ \\\\ans= \lim_{h \to 0}\ \frac{(a+h)\ sin a-a\ sin a\ cosh-a\ cosa\ sinh}{h}\\\\=\lim_{h \to 0}\ \frac{h\ sina+a\ sin a\ (1-cos\ h)-a\ cosa\ sinh}{h}\\\\=\lim_{h \to 0}\ \frac{h\ sina+2a\ sin a\ sin^2 \frac{h}{2} - a\ cosa\ sinh}{h}\\\\=\lim_{h \to 0}\ sin\ a+a* sin\ a*\frac{sin\frac{h}{2}}{\frac{h}{2}}*sin\frac{h}{2}-a\ cosa*\frac{sin\ h}{h}\\\\=sin\ a+a\ sina*1*0-a\ cos\ a*1\\\\=sin\ a - a\ cos\ a$


Answer = sin a - a cos a