cotx=125⇒cosx=13−5=2cos22x−1
cos(2x)=−132 or 132 (rejected)
{∵2x∈(2π,43π)}
(sin7x2sin13x+cos7x2cos13x)+(sin7x2cos13x−cos7x2sin13x)
cos(7x−213x)+sin(7x−213x)
cos2x+sin(2x)
133−132=131
If cotx=125 for some x∈(π,23π), then sin7x(cos213x+sin213x)+cos7x(cos213x−sin213x) is equal to
Held on 24 Jan 2026 · Verified 6 Jul 2026.
264
266
135
131
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