if f(x) = 1+ sin x +(sin x)3 + (sin x)5+........

x(-/2 , /2). then find its range

It's an infinite GP having common ratio = . We have, from the sum to infinite terms of a GP having |r| < 1 :

.

Thus. we have the range of f(x) as .

heyya it shud b:

f(x) = 1 +{ sinx / 1 - sin²x}

       = 1 + sinx/cos²x

       range(-inf,inf)---------->>1 is included!!

cheers!

sinx----->>(-1,1)

cos^2 x--->>(0,1]

so we'll have -infinity too

thanks dude