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Question : 52 of 160
Marks:
+1,
-0
Solution:
Consider the given function.
x=A‌cos(nt+α) Differentiate the above function with respect to
t ‌‌=A‌‌‌cos(nt+α) =−A‌sin(nt+α)‌‌(nt+α) =−‌‌| xn‌sin(nt+α) |
| cos(nt+α) |
=−nx‌tan(nt+α) Again differentiate with respect to
t ‌‌=−[nx‌‌‌tan(nt+α)+tan(nt+α)‌‌nx] ‌‌=−[nxsec2(nt+α)‌‌(nt+α)+tan(nt+α)‌‌×n] ‌‌=−[nxsec2(nt+α)n+n‌tan(nt+α)‌x−nx‌tan(nt+α)] ‌‌=−[n2xsec2(nt+α)−n2xtan2(nt+α)] Solve further
‌‌=−n2×[sec2(nt+α)−tan2(nt+α)] ‌‌=−n2x×1=−nx2 ‌‌+n2x=0
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