Carter is playing a video game. He needs to score more than 100 points to move on to the next level. Write an inequality to show
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Answer:
Step-by-step explanation:
please note that to find but α+β+γ in other words the sum of α,β and γ not α,β and γ individually so it's not an equation
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we want to find all possible values of α+β+γ when <u>tanα+tanβ+tanγ = tanαtanβtanγ</u><u> </u>to do so we can use algebra and trigonometric skills first
cancel tanγ from both sides which yields:
factor out tanγ:
divide both sides by tanαtanβ-1 and that yields:
multiply both numerator and denominator by-1 which yields:
recall angle sum indentity of tan:
let α+β be t and transform:
remember that tan(t)=tan(t±kπ) so
therefore <u>when</u><u> </u><u>k </u><u>is </u><u>1</u> we obtain:
remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus
recall that if we have common trigonometric function in both sides then the angle must equal which yields:
isolate -α-β to left hand side and change its sign:
<u>when</u><u> </u><u>i</u><u>s</u><u> </u><u>0</u>:
likewise by Opposite Angle Identity we obtain:
recall that if we have common trigonometric function in both sides then the angle must equal therefore:
isolate -α-β to left hand side and change its sign:
and we're done!