Trigonometric sums and summation formulas have long served as essential tools for elucidating periodic phenomena across mathematics and the physical sciences. These techniques entail the explicit ...

Sec(a-b) = cos(a+b) / cos^2a - sin^2b I'm trying to prove this, by turning the left side into the right. I am stuck. Presumably you have already done the sum and difference formulas for sin and cos.

In 2022, two high school students created a trigonometric proof of the Pythagorean Theorem—something that’s only ever been accomplished by a few professional mathematicians. Now, a new article not ...

The Pythagorean Theorem—discovered by the Greek mathematician Pythagoras in the 6th century BCE—is a cornerstone of mathematics. Simply stated as a 2 + b 2 = c 2, the theorem posits that the sum of ...

We utilize formulas for basic hypergeometric series to derive identities and formulas for negative degree q-Bernstein bases, including the Marsden identity, the partition of unity property, the ...

Two high school students have proved the Pythagorean theorem in a way that one early 20th-century mathematician thought was impossible: using trigonometry. Calcea Johnson and Ne’Kiya Jackson, both at ...

This is an updated version of a story first published on May 5, 2024. For many high school students returning to class, it may seem like geometry and trigonometry were created by the Greeks as a form ...