Help Solving Trig Equation: Cos70°cos20°-sin70°sin20°

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The discussion focuses on solving the trigonometric equation Cos70°cos20° - sin70°sin20°. A participant seeks a formula for cos(a+b), which is expressed as cos a • cos b - sin a • sin b. They struggle to find equivalent angles for 70° and 20°. Another participant points out that cos(20+70) equals cos(90), which simplifies the equation. The conversation highlights the application of trigonometric identities in solving equations.
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Cos70°cos20°-sin70°sin20°

I can't find any of these angles that are equivalent to the basic angles. Thanks
 
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Do you know a formula for cos(a+b) in terms of the trig functions evaluated at a and b?
 
Cost(a+b)=cos a • cos b - sin a • sin b
 
I don't know which angles are equivalent to 70° nor 20°
 
But you know cos(20+70)=cos(90), right?
 
Whoops. Thanks
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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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