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Question Number 48264 by Abdo msup. last updated on 21/Nov/18

l e t f (x) = \int_{0}^{2 π} \frac{s i n (2 t)}{1 + x c o s (t)} d t

1) f i n d a e x p l i c i t f o r m o f f (x)

2) f i n d a l s o g (x) = \int_{0}^{2 π} \frac{s i n (2 t) c o s t}{{(1 + x c o s t)}^{2}} d t

3) f i n d t h e v a l u e o f \int_{0}^{2 π} \frac{s i n (2 t)}{1 + 3 c o s (t)} d t a n d

\int_{0}^{2 π} \frac{c o s t s i n (2 t)}{{(1 + 3 c o s t)}^{2}} d t .