A Simple Trig TRICK Solves This Complex Equation!

In this video, we solve the intriguing math olympiad algebra equation 1/x² + 1/(4 - √3·x)² = 1 using a clever trigonometric substitution: sin y = 1/x and cos y = 1/(4 - √3·x). This transformation reveals hidden trigonometric identities that simplify the expression and lead us to the solution step by step. Ideal for high school students, math Olympiad aspirants, and math enthusiasts, this tutorial demonstrates how advanced algebra and trigonometry techniques can be combined to solve nonlinear equations efficiently. Whether you're preparing for competitive exams or just love a good math puzzle, this problem is sure to stretch your thinking and sharpen your skills.

Timestamps:
00:00 – Introduction to the problem
00:40 – Step 1: Analyzing the equation structure
01:36 – Step 2: Substituting sin y = 1/x and cos y = 1/(4 - √3·x)
02:10 – Step 3: Substituting x = 1/siny into the equation for cosy and simplifying.
04:18 – Step 4: Solving the trigonometric equation
09:40 – Step 5: Back-substituting to find x
11:05 – Final thoughts

#maths #Algebra #MathOlympiad #TrigonometryHack #AlgebraTricks

Видео A Simple Trig TRICK Solves This Complex Equation! канала NonsoMaths