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Find all values of a satisfying this sin7a = sina + sin3a

Find all values of a satisfying this
sin7a = sina + sin3a

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:Hello student, please find answer to your question
sin7a = sina + sin3a
sin7a - sina = sin3a
sinc - sind = 2cos(\frac{c+d}{2}).sin(\frac{c-d}{2})
2cos4a.sin3a = sin3a
sin3a(2cos4a-1) = 0
sin3a = 0
3a = 2n\pi
a = \frac{2n\pi }{3}
cos4a = \frac{1}{2}
\Rightarrow 4a = 2n\pi \pm \frac{\pi }{3}
\Rightarrow a = \frac{n\pi }{2} \pm \frac{\pi }{12}

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