Find the exact value please show steps sin alpha 45 pi2 Sol

Find the exact value please show steps sin alpha = 4/5, pi/2

Solution

given sin =4_/5,_/2<< ,cos=12_/13,0<<_/2

=>cos=-(5²-4²)_/5 ,sin=(13²-12²)_/13

=>cos=-3_/5 ,sin=5_/13

sin(-)=sincos -cossin

sin(-)=(4_/5)(12_/13)-(-3_/5)(5_/13)

sin(-)=(48_/65)+(15_/65)

sin(-)=(63_/65)