The Pythagorean Identity: Exploring the Fundamental Relationship Between Sin and Cos

sin^2x + cos^2x =

The equation you have written, sin^2x + cos^2x, represents the trigonometric identity known as the Pythagorean identity

The equation you have written, sin^2x + cos^2x, represents the trigonometric identity known as the Pythagorean identity.

According to the Pythagorean identity, for any angle x, the sum of the squares of the sine and cosine of that angle is always equal to 1. Mathematically, it can be expressed as:

sin^2x + cos^2x = 1

This identity is true for all values of x, and it is a fundamental relationship between the sine and cosine functions in trigonometry. It is derived from the Pythagorean theorem in geometry, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

So, no matter what value you substitute for x, the sum of the squares of the sine and cosine of that angle will always be 1.

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