Sin15degrees prove this by compound angles.

Question

sin15

Answer 1

To label a triangle "a" is the shortest side; "b" is the mid size side; "c" is the hypotenuse.

The angles are "alpha"opposite from "a".

"beta" "b".

"gamma" "c".

15 deg sounds like "alpha". Sin "alpha"=a/c.

"beta"=b/c.

"gamma"=1.

These formulas are in reference to a rt triangle. Sin 15deg=.2588.........=sin165deg.

Answer 2

Nothing to prove, hopefully you mean "evaluate"

Use half-angle formula for sin: sin (A/2) = +/- sqrt ((1-cos A)/2)

Take A=30. In the formula above, use the positive square root, since 15 deg is in Quadrant I.

sin (15)= sin(30/2) = sqrt ((1-cos30)/2) .

Note: cos 30 = sqrt(3)/2. Continue the algebra to obtain the final answer.