Trigonometry Level UP: Solving (cos x)^8 + (sin x)^8 with The cos(4x) Trick
Автор: MathNoPanic
Загружено: 2025-12-03
Просмотров: 9
Welcome to a true trigonometric challenge! This problem, (cos x)^8 + (sin x)^8 = 97/128 on the domain in the interval [0, pi/2], looks impossible, but it has an elegant solution.
The MathNoPanic Method:
We demonstrate a step-by-step method using repeated Power Reduction to collapse the eighth degree equation down to a simple quadratic equation in terms of cos(4x). We use the Balance Method to derive the necessary identities, like the (sin a)^2 reduction formula, and successfully navigate the resulting complex quadratic equation (y^2 + 14y - 29/4 = 0) to find the final two valid solutions.
📌 Key Identities Used: Pythagorean Identity, Square of a Sum, Sine Double Angle, and Power Reduction Formula.
This problem is famous for having an almost-impossible answer. Did you predict the final solutions of pi/12 and (5pi)/12? Let me know your score! 👇
🎶 Credit: White River - Aakash Gandhi_join.
#TrigonometryChallenge #PowerReduction #Cos8x #MathHack #AdvancedMath #TrigIdentities #QuadraticFormula #UnitCircle #MathNoPanic #CalculusPrep
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