Question

sin 15 degree=^3-1/2^2.prove it

Answer 1

cos2x=1-2sin^(2)x

put x=15

cos30=1-2sin^2{15}
2sin^(2){15}=1-c0s30

Answer 2

\[2\sin^215=1-\sqrt3/2=\frac{2-\sqrt3}{2}\]\[\sin^215=\frac{2-\sqrt3}{4}\]

Answer 3

\[\sin15=\frac {\sqrt{2-\sqrt3}}2\]

Answer 4

sin(15) = sin(45 - 30) = sin45cos30 - cos45sin30

= (1/sqrt2)(sqrt3/2) - (1/sqrt2)(1/2)

= (sqrt3-1)/(2sqrt2)

= sqrt2(sqrt3 - 1)/4

Answer 5

\[\sin15=\frac{\sqrt{4-2\sqrt3}}{2\sqrt2}=\frac{\sqrt{(\sqrt3-1)^2}}{2\sqrt2}=\frac{\sqrt3-1}{2\sqrt2}\]