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Question : 59 of 160
Marks:
+1,
-0
Solution:
Step 1 - Expand the numerator using small-angle approximations
As
x⟶0 :
cos‌x=1−‌+O(x4),‌‌cos‌2‌x=1−2x2+O(x4)Multiply:
cos‌x‌cos‌2‌x‌=(1−‌)(1−2x2)+O(x4)=‌1−2x2−‌+O(x4)=‌1−‌x2+O(x4)Thus:
1−cos‌x‌cos‌2‌x=‌x2+O(x4)Step 2 - Expand the denominator
sin‌x=x+O(x3)‌‌⇒‌‌sin‌2x=x2+O(x4)Step 3 - Form the ratio
‌| 1−cos‌x‌cos‌2‌x |
| sin‌2x |
=‌⟶‌
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