Question
Solve that cos2x +sin2x=1 using a right angles A
Answers
GPT 3.5
To solve the equation cos2x + sin2x = 1, we can make use of the Pythagorean identity for sine and cosine:
sin2x = 1 - cos2x.
Substituting this into the original equation, we get:
cos2x + (1 - cos2x) = 1.
Simplifying, we have:
cos2x + 1 - cos2x = 1.
The terms cos2x and -cos2x cancel out, leaving us with:
1 = 1.
This is a true statement, meaning that for any value of x, the equation cos2x + sin2x = 1 holds true. Therefore, the solution to this equation is any real number.
sin2x = 1 - cos2x.
Substituting this into the original equation, we get:
cos2x + (1 - cos2x) = 1.
Simplifying, we have:
cos2x + 1 - cos2x = 1.
The terms cos2x and -cos2x cancel out, leaving us with:
1 = 1.
This is a true statement, meaning that for any value of x, the equation cos2x + sin2x = 1 holds true. Therefore, the solution to this equation is any real number.