Is 2tan2b the Simplified Form of tan(45° + b) - tan(45° - b)?

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The discussion focuses on the simplification of the expression tan(45° + b) - tan(45° - b). The initial attempt led to confusion regarding the correct numerator, which was clarified to be just 4 tan b, rather than including an additional 1. The correct denominator was acknowledged as valid, and it was noted that this simplification leads to the final result of 2 * tan 2b. The conversation emphasizes the importance of accurately applying tangent sum and difference identities for proper simplification. The conclusion confirms that the simplified form is indeed 2tan2b.
philipp2020
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hi

i have a question on a simplification

tan (45° + b) - tan (45° -b)

Then I put on both sides the Theorems for Addition. But I am not sure if my result is right. What is most possible simplification here?

is it 1 + 4 tan b / 1 - tan^2 b ?

Thanks very much for an answer.

Greetings

Philipp
 
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Double check the tangent sum and difference identities. Your denominator is good, but I can't figure out what mistake you could have made to get the numerator that you did.

If you get the numerator correct, there's another identity that allows you to simplify the fraction.
 
ah so the numerator is only 4 tan b and not plus 1 yes...

oh ok... i see

then at the end it will be just 2 * tan 2b
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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