Expert: Ahmed Salami - 4/7/2009

Question
sin^4(a)+cos^4(a)=1-2sin^2(a)cos^2(a)

Answer
Hi Khoo,
sin^2(a) + cos^2(a) = 1    (an identity)
therefore, sqyaring both sides
[sin^2(a) + cos^2(a)]^2 = 1
[sin^2(a) + cos^2(a)][sin^2(a) + cos^2(a)] = 1
sin^4(a) + sin^2(a).cos^2(a) + cos^2(a).sin^2(a) + cos^4(a) = 1
sin^4(a) + 2sin^2(a).cos^2(a) + cos^4(a) = 1
sin^4(a) + cos^4(a) = 1 - 2sin^2(a).cos^2(a)

Regards