Find the number of distinct solutions of equation sin5θcos3θ=sin9θcos7θ,
θ ε [0,π/2]
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4 Answers
106sin5@cos3@=sin9@cos7@
=> sin8@ + sin2@ = sin16@ + sin2@
=> sin8@ = sin16@
or 16@ = n∩ + (-1)n8@
seeing the various cases,
8@ = 2m∩, or 24@ = (2k+1)∩
@ = 2m∩/8 = 0, ∩/4, ∩/2 OR @ = ∩/24, ∩/8, 5∩/24, 7∩/24, 9∩/24, 11∩/24
So 9 solutions
106yeah 9 solutions ... din see that the interval was ∩/2 included...