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Answer:
see explanation
Step-by-step explanation:
If A +B = 45° then tan(A+B) = tan45° = 1
Expanding (1 + tanA)(1 + tanB)
= 1 + tanA + tanB + tanAtanB → (1)
Using the Addition formula for tan(A + B)
tan(A+B) = = 1 ← from above
Hence
tanA + tanB = 1 - tanAtanB ( add tanAtanB to both sides )
tanA + tanB + tanAtanB = 1 ( add 1 to both sides )
1 + tanA + tanB + tanAtanB = 2
Then from (1)
(1 + tanA)(1 + tanB) = 2 ⇒ proven
<h2>Maneuvering an equals sign</h2><h3>Concept</h3>
Learn the rules and implications of moving numbers across an equals sign to combine like terms.
<h3>Utilization</h3>When you move a negative number across an equals sign (in incredibly linear equations), you should always add it, the inverse (subtract) goes for positive numbers.
x = -11