Question

If sinx= 12/13 and y=4/5, where pi/2 greater than x greater than pi, find the value of sin (x+y).Brainly

Answer 1

We know that ,

sin ( x + y ) = sin x * cos y + cos x * sin y

but ,

sin X = 12 -------------- 1)

13

sin y = 4 -------------- 2)

5

π < X < π ,. :. X lies in 2nd quadrant .

2

:. sin^2 X + cos^2 X = 1

:. cos^2 X = 1 - sin^2 X

= 1 - ( 12 )^2

( 13 )^2

= 1 - 144

169

= 169 - 144

169

:. cos^2 x = 25

169

taking sq. rt.,

:. cos X = - 5

13

------ ( as X lies in 2nd quadrant ,

cos is - ve. )

NOW,

:. sin^2 y + cos^2 y =1

:. cos^2 y = 1 - sin^2 y

= 1 - ( 4 )^2

( 5 )^2

= 1 - 16

25

= 25 - 16

25

:. cos^2 y = 9

25

taking sq. rt.

:. cos y = - 3

5

------ ( as X lies in 2nd quadrant ,

cos is - ve. )

FINALLY ,

sin ( X + y ) = sin X * cos y + cos X * sin y

= 12 * -3 + -5 * 4

13 5 13 5

= -36 + -20

65 65

= -36-20

65

= - 56

65