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Please solve the question in the attachment...... .... ANS is coming 1/2....... .

Please solve the question in the attachment...... .... ANS is coming 1/2....... . 

Question Image
Grade:12th pass

1 Answers

Aditya Gupta
2080 Points
3 years ago
let cosx=c and sinx=s and y=root((1-c)+root((1-c)+root(....)))
then y^2= 1-c+y [note here that y(y-1) > 0 or y is greater than1]
 y^2-y+c-1=0
y=(1+-root(5-4c))/2
as y is greater than 1, negative sign is rejected.
so y=(1+root(5-4c))/2
now y-1=(–1+root(5-4c))/2
rationalising we get
2(1-c)/(1+root(5-4c))
plug in the limit we have
2/2 * (1-c)/x^2
=(1-c)/s^2*(s/x)^2
=(1-c)/(1-c)(1+c)*1
=1/(1+c)
=1/(1+1)
=1/2
 

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