You’ve seen this in every math class:

 Dr Muhammad Salah

 

٤٥ د ·

You’ve seen this in every math class:

sin(a ± b) = sin a cos b ± cos a sin b

sin(2a) = 2 sin a cos a

cos(2a) = 1 − 2 sin²(a)

But did you know these formulae came from a Muslim scholar 1000 yrs ago.

Meet Abū al-Wafā al-Būzjānī, the genius who shaped Trigonometry.

Abū al-Wafā Būzhjānī (d. 998) was a Persian Muslim mathematician and astronomer from Khorasan. Born in Būzjān (near Nishapur, Iran), Būzhjānī showed early brilliance in mathematics and geometry.

He later moved to Baghdad, then the heart of the Islamic Golden Age — a city of scholars, libraries, and observatories.

In Baghdad, he became one of the leading scientists of the House of Wisdom (Bayt al-Ḥikmah).

Here, he studied Greek works like Euclid and Ptolemy, and expanded them far beyond their original limits. His Contributions to Mathematics:

He established several Trigo. identities such as [𝒔𝒊𝒏(𝒂±𝒃)] in their modern form:

{𝙨𝙞𝙣(α ± β)= 𝙎𝙞𝙣α 𝘾𝙤𝙨β ± 𝘾𝙤𝙨α 𝙎𝙞𝙣β}

{𝙨𝙞𝙣(𝙖 + 𝙗) = 𝙎𝙞𝙣(𝙖)𝘾𝙤𝙨(𝙗) + 𝘾𝙤𝙨(𝙖)𝙎𝙞𝙣(𝙗)}

{𝘾𝙤𝙨(2𝙖) = 1-2𝙨𝙞𝙣²(𝙖)}

{𝙎𝙞𝙣(2𝙖) = 2𝙎𝙞𝙣(𝙖) 𝘾𝙤𝙨(𝙖)}

He compiled tables of sines and tangents at 15° intervals, introduced secant and cosecant,

and explored the relationships between all six trigonometric lines. His work made both mathematics and astronomy quantitatively precise.

He also studied geometry, arithmetic, and number theory, writing detailed commentaries on al-Khwārizmī and Diophantus.