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Let f(theta)=1/(1+(cottheta)^2) , and S=...

Let `f(theta)=1/(1+(cottheta)^2)` , and `S=sum_(theta=1^0)^(89^0)f(theta),` then the value of `sqrt(2S-8)` is___________

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The correct Answer is:
44.5
We have ,`f(theta)=((sintheta)^x)/((costheta)^x+(sintheta)^x)`
`rArr f(theta)+f(pi/2-theta)=1`.
`:. S=underset(theta=1^@)overset(89^@)sumf(theta)=f(1^@)+f(2^@)+...+f(88^@)+f(89^@)`
`=(ubrace(1+1+1+.........+1)_("44 times"))+1/2=44+1/2=89/2`
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