If sin x = `(15)/(17)` and cos y = `(12)/(13),0 lt x lt (pi)/(2) , 0 lt y lt (pi)/(2)`,
find the values of
sin (x + y)

If sin x = (15)/(17) and cos y = (12)/(13),0 lt x lt (pi)/(2) , 0 lt y lt (pi)/(2) , find the values of cos(x - y)

If sin x = (15)/(17) and cos y = (12)/(13),0 lt x lt (pi)/(2) , 0 lt y lt (pi)/(2) , find the values of tan(x + y)

If sin x=(12)/(13) "and sin " y= (4)/(5) " where " (pi)/(2) lt x lt pi " and " 0 lt y lt .(pi)/(2) find the values of (i) " sin " (x+y) " "(ii) " cos " (x+y) " "(iii) " tan " (x-y)

If sin x =(3)/(5) " and " 0 lt x lt (pi)/(2) find the value of tan (x)/(2)

If sec x =- (13)/(12) and (pi)/(2) lt x lt pi , find the value of sin 2x

if cos x= (-sqrt(15))/(4) " and " (pi)/(2) lt x lt pi find the value of sin x .

if cos x= (-sqrt(15))/(4) " and " (pi)/(2) lt x lt pi find the value of sin x .