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Trigonometry> Find all values of a satisfying this sin7...

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

Kawal , 11 Years ago

Grade 11

1 Answers

Jitender Singh

Ans:Hello student, please find answer to your question
$sin7a = sina + sin3a$
$sin7a - sina = sin3a$
$sinc - sind = 2cos(\frac{c+d}{2}).sin(\frac{c-d}{2})$
$2cos4a.sin3a = sin3a$
$sin3a(2cos4a-1) = 0$
$sin3a = 0$
$3a = 2n\pi$
$a = \frac{2n\pi }{3}$
$cos4a = \frac{1}{2}$
$\Rightarrow 4a = 2n\pi \pm \frac{\pi }{3}$
$\Rightarrow a = \frac{n\pi }{2} \pm \frac{\pi }{12}$

Approved

Last Activity: 11 Years ago

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