find the Product of {1 + (cotx)^2 }{1 - cosx}{1 + cosx} and also find the value of product at x= 45°
pls tell the answer correctly
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Answer:
Let, L=
x→0
lim
(
1+cosx
1+cotx
)
1/cosx
Clearly form of the limit is 1
∞
, So
L=
x→0
lim
(1+
1+cosx
1+cotx
−1)
1/cosx
=
x→0
lim
(1+
1+cosx
cotx−cosx
)
cotx−cosx
1+cosx
.
(1+cosx)cosx
cotx−cosx
=e
x→0
lim
(1+cosx)cosx
cotx−cosx
=e
x→0
lim
(1+cosx)
sinx
1
−1
=e
0
=1
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