Question

Prove that cos^2(15) + cos^2(45) + cos^2(75) = 3/2

Answer 1

man if you change cos^2(15) into sin then you will get sin^2(75) as there is cos^2(75) therefore both of them will be equal to 1 as sin^2x+ cos^2x =1
therefore you will be left with 1 + cos^2(45)
the value of cos 45 is 1/√2
as it has square it will make it 1/2
you will be left with 1+1/2
which is equal to 3/2

Answer 2

cos^2(15)+cos^(45)+cos^2(75)=cos^2(45-30)+cos^2(45)+cos^2(45+30)=cos^2(45)-cos^2(30)+cos^2(45)+cos^2(45)+cos^2(30)=1/2-3/4+1/2+1/2+3/4=3/2