Pre-Calculus - Find All of the Solutions of an Equation Using the Double Angle Formulas

The video tutorial explains how to solve a trigonometric equation involving sine and cosine functions. The instructor begins by introducing the problem and discussing the lack of double or half angles. They then apply trigonometric identities to simplify the equation, transforming it into a single trigonometric function. The instructor solves the simplified equation and finds all possible solutions within a given interval. The tutorial concludes with a discussion on methods for solving similar problems using multiple angle formulas.

What is the initial equation the teacher is trying to solve?

• 2sin(X)cos(X) = 1

• sin^2(X) - cos^2(X) = 1

• 4sin(X)cos(X) = 1

• sin(X) + cos(X) = 1

Which trigonometric identity is used to simplify the equation?

• sin^2(X) + cos^2(X) = 1

• tan(2X) = 2tan(X)/(1-tan^2(X))

• cos(2X) = cos^2(X) - sin^2(X)

• sin(2X) = 2sin(X)cos(X)

What is the simplified form of the equation after applying the double angle formula?

• sin(2X) = 2

• sin(2X) = 1/2

• cos(2X) = 1/2

• tan(2X) = 1/2

What are the primary solutions for 2X when sin(2X) = 1/2?

• π/2 and 3π/2

• π/3 and 2π/3

• π/4 and 3π/4

• π/6 and 5π/6

How are all solutions for X found after determining the primary solutions for 2X?

• By adding multiples of π

• By subtracting multiples of π

• By adding multiples of 2π

• By subtracting multiples of 2π