MHB Solving Trig Identity: Sin[1/2 sin^−1 (x)] = 1/2 X (sqr(1+x) –sqr(1-x))

[DUC_123]

Good morning, may I possibly get a clue into solving this problem : check this identity: sin[1/2 sin^−1 (x) ]=1/2 X (sqr(1+x) –sqr(1-x)). I tried to say "2y=sin^−1 (x)", Then f=sin(y), then "x=sin(2y)", x=2sin(x) X cos(x), but I can't find further. Thank you very much.

 

[DUC_123]

Good morning, may I possibly get a clue into solving this problem : check this identity: sin[1/2 sin^−1 (x) ]=1/2 X (sqr(1+x) –sqr(1-x)). I tried to say "2y=sin^−1 (x)", Then f=sin(y), then "x=sin(2y)", x=2sin(y) X cos(y), but I can't find further. Thank you very much.

 

[topsquark]

Please, no x's or X's. If you must use something use *. Many people just use a space, such as in x = 2 sin(y) cos(y).

-Dan