expres the following as sums and differences of sines or cosines

Question

cos8t * sin2t

sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

replacing by by -b and using that
cos(-b)= cos(b)
sin(-b)= -sin(b)

gives:

sin(a-b) = sin(a)cos(b) - cos(a)sin(b)

Add the two equations:

sin(a+b) + sin(a-b) = 2sin(a)cos(b)-->

sin(a)cos(b)= 1/2 [sin(a+b) + sin(a-b)]

who found trigonometry?

Answer 1

Trigonometry was not discovered by a single person. Its development spans thousands of years and involves contributions from various civilizations, including the Babylonians, Egyptians, Greeks, and Indians. Some notable mathematicians who contributed to the development of trigonometry include Hipparchus, Menelaus, Ptolemy, Aryabhata, and Al-Khwarizmi.