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[Solved] Prove the trigonometric problem

 
Trigonometry 1 & 2
Last Post by Staff 4 years ago
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June 15, 2021 12:47 pm
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(@armor)
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June 15, 2021 12:47 pm
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

Proof: Applying the equal radio theorem, we have     \small \frac{b}{cos2\alpha }=\frac{a+c}{cos\alpha +3cos\alpha }\neq 0,

Since  \small cos\alpha \neq 0,     

\small cos2\alpha \neq 0\Rightarrow \frac{b}{cos2\alpha }=\frac{a+c}{2cos\alpha cos2\alpha }\neq 0.

In particular, \small b\neq 0, cos\alpha =\frac{a+c}{2b}.

Therefore  \small sin^2\frac{\alpha }{2}=\frac{1-cos\alpha }{2}=\frac{1}{2}(1-\frac{a+c}{2b})=\frac{2b-a-c}{4b}.

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