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Trigonometry 2
 
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[Solved] Trigonometry 2

 
Trigonometry 1 & 2
Last Post by Staff 4 years ago
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June 15, 2021 2:29 pm
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(@armor)
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June 15, 2021 2:30 pm
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

Multiplying the two equations together to obtain

 \small mn=tan^2\alpha -sin^2\alpha =tan^2\alpha (1-cos^2\alpha )=tan^2\alpha sin^2\alpha     (1)

Adding the two equations:

 \small 2tan\alpha =m+n\Rightarrow tan\alpha =\frac{m+n}{2}      (2)

Using subtraction for the two equations:

\small 2sin\alpha =m-n\Rightarrow sin\alpha =\frac{m-n}{2}    (3)

Substituting (2) and (3) into (1):

\small mn=(\frac{m+n}{2})^2(\frac{m-n}{2})^2\Rightarrow m^2-n^2=4\sqrt{mn} .

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