Question

Nilai dari sim^2 31derajat +sin^2 59derajat adalah

Answer 1

Ingat : a^2+b^2 = (a+b)^2 - 2ab

sin^2 31+sin^2 59
= (sin 31+sin 59)^2 - 2sin 31.sin 59
= (2 sin 45 cos 14)^2 - 2sin 31.sin 59
=(√2. cos 14)^2 + cos 90 - cos 28
=2. cos^2 14 - cos 28
=2. cos^2 14 - cos 2.14 ----->> cos 2A = cos^A - 1
=2. cos^2 14  - (cos^2 14 -1)
=2. cos^2 14  - cos^2 14 + 1
=cos^2 14  + 1