sin^2x+cos^2x =
1
1
Explanation:
The sum of two squares sin^2x and cos^2x is always equal to 1, which can be mathematically expressed as:
sin^2x + cos^2x = 1
This is a fundamental identity in trigonometry which holds true for any angle x in radians or degrees. It is derived from the Pythagorean theorem, where sinx, cosx and 1 are the sides of a right-angled triangle, with the angle x being its acute angle. Therefore, the sum of the squares of the two shorter sides (sin^2x + cos^2x) is equal to the square of the hypotenuse (1) in accordance with the Pythagorean theorem. This identity is extremely useful in many branches of mathematics, science and engineering, especially in solving problems related to geometry, mechanics, waves and oscillations, among others.
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