Which is equivalent to the expression below? 3p+4+p+12+3q
1 answer:
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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!
Answer:
No, They are not equivalent
Step-by-step explanation:
The two expressions are only said to be equivalent if they are the same regardless of whatever value the variable(s) is.
The variable in this question is x.
To prove this, we equate both expressions:
This shows that they have the same value ONLY when x is 1.
This is why Andre says that they are equivalent, but they are not.