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Grade: 12th pass
        PleaPl help me with the question given in the image attachment.
6 months ago

## Answers : (2)

Arun
22545 Points
							Lim x->a (cos x - cos a / cot x - cot a) = Lim x->a (cos x - cos a) / [(cos x sin a - cos a sin x)/(sin x sin a)] = Lim x->a (-2sin((x-a)/2)sin((x+a)/2)) / [(sin(a-x))/(sin x sin a)] = sin^3 a --------- Ideas: cos x - cos a = cos[(x+a)/2 + (x-a)/2] - cos[(x+a)/2 - (x-a)/2] = -2sin((x-a)/2)sin((x+a)/2)

6 months ago
Samyak Jain
333 Points
							 lim   (cosx – cosa) / (cotx – cota)  It is of 0 by 0 form. Simplifying it we can calculate the limit.x$\dpi{80} \rightarrow$aWe know cosx – cosa = 2 sin(x+a)/2 sin(a – x)/2  andcotx – cota = cosx/sinx – cosa/sina = (sina cosx – cosa sinx) / sinx sina = sin(a – x) / sinx sina$\dpi{80} \therefore$ lim (cosx – cosa) / (cotx – cota) = lim [2 sin(x+a)/2 sin(a – x)/2] / [sin(a – x) / sinx sina] x$\dpi{80} \rightarrow$a                                            x$\dpi{80} \rightarrow$a = lim  [2 sin(x+a)/2 sin(a – x)/2 . sinx sina ] / [2 sin (a – x)/2 cos(a – x)/2 ]  x$\dpi{80} \rightarrow$a= lim  sin(x+a)/2 . sinx sina / cos(a – x)/2  =  sina lim sin(x+a)/2 . sinx / lim cos(a – x)/2 x$\dpi{80} \rightarrow$a                                                                 x$\dpi{80} \rightarrow$a                         x$\dpi{80} \rightarrow$a= sina sin(a+a)/2 . sina / cos(a – a)/2  =  sina sina .sina / cos0= sin3a

6 months ago
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