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Question : 129 of 180
Marks:
+1,
-0
Solution:
With the help of group of
cot‌x, we know that When
x∈(0,‌]∪(π,‌], then
cot‌x≥0‌∴‌‌|cot‌x|=cot‌x+‌‌⇒cot‌x=cot‌x+‌⇒‌=0⇒ No solution exist. . . . (i)
When
x∈(‌,π)∪(‌,2π), then
cot‌x<0‌|cot‌x|=cot‌x+‌∴‌−cot‌x‌=cot‌x+‌⇒−2‌cot‌x‌=‌⇒‌cos‌x‌=‌⇒x=‌ . . . (ii)
∴ From Eqs. (i) and (ii), only one solution exists.
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