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trigonometric limit but i find difficulties in solving this question

trigonometric limit but i find difficulties in solving this question
 

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Grade:12

1 Answers

Aditya Gupta
2081 Points
4 years ago
hello swayam this is an ez ques.
simply put 1 – x= y
so we have lim y tends to 0 y*tan(pi(1 – y)/2)
=  lim y tends to 0 y*tan(pi/2 – piy/2)
=  lim y tends to 0 y*cot(pi*y/2)
=  lim y tends to 0 y/tan(piy/2)
now put y= 2z/pi
we have
lim z tends to 0 (2z/pi)/tanz
= 2/pi*lim z tends to 0 (z)/tanz
= 2/pi (as lim z tends to 0 (z)/tanz= lim z tends to 0 (z)/sinz*lim z tends to 0 cosz= 1*1= 1)
kindly approve :)

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