if `sinx=3/5 , cosy= -12/13` where `pi/2ltxlt pi` and="" `pi/2ltyltpi ` then show that sin(x+y) =`-56/65`

if sin x=(3)/(5),cos y=-(12)/(13) where (pi)/(2)

If sinA=3/5, cosB=-12/13 , where A in 0,pi/2[,B in]pi,(3pi)/2 ,then evaluate the following: i) sin(A-B) ii) cos(A-B) iii) tan(A+B)

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 cos x=(3)/(5) " and cos " y=(-24)/(25) " where " .(3pi)/(2) lt x lt 2 pi " and " pi lt y lt .(3pi)/(2) find the values of (i) " sin (x+y) "" ""(ii) cos (x-y) "" ""(iii) tan (x+y) "

lf (pi)/(4)ltxlt(pi)/(2) then write the value of sqrt(1-sin2x) is

If 13 sin alpha = 12, where pi//2 lt alpha lt pi, and 3 sec beta = 5, where 3pi//2 lt beta lt 2pi , evaluate : 5tan alpha+3 tan^(2)beta.

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

If sin theta = (12)/(13) (0 lt theta lt (pi)/(2)) and cos phi = (-3)/(5) (pi lt phi lt (3pi)/(2)) then 65 sin (theta + phi) + 60 equals to "_______"