Please help me solve the problem of given limit based question.

hello pushpa, i would request you to ask maths ques in the math section and not in zoology section.

now, the problem can be solved in two ways: 

(i) we see that numerator and denominator are of zero/zero form. so we can apply l hospital rule and differentiate wrt h.

we get lim h tends to 0 [cos(x+h)*1 – 0]/1

= lim h tends to 0 cos(x+h)

= cosx

another method is to use the formula sina – sinb= 2sin(a – b)/2cos(a+b)/2

and then use the standard result lim y tends to 0 siny/y= 1.