Question

if sin (x + y) =1 and cos (x-y) = √3/2 then find the values of x and y.

Answer 1

Step-by-step explanation:

Sin ( x + y ) = Sin ( 90 ) and Cos ( x - y) = Cos ( 30 )

bcoz. Sin ( 90 ) = 1. and Cos ( 30 ) = √3 / 2

=>. x + y = 90....... equation 1

and

x - y = 30..... equation 2

Adding both the equations

x = 60 and. y = 30

Answer 2

Answer:
If Sin(x+y)= 1 and Cos (x-y) = √3/2, then the values of x and y are 60° and 30° respectively

Step-by-step explanation:

Given

Sin(x+y)= 1

We know that, Sin 90° = 1

So, sin (x+y) = sin 90°

That is x + y = 90°
x = 90-y

Also given

Cos (x-y) = √3/2

We know that cos 30°= √3/2

So, cos(x-y) = cos 30°

That is, x-y = 30°

Substitute x= 90-y

So, x -y = 90-y-y = 90-2y

So, 90-2y = 30

2y = 90-30

2y = 60

y = 60/2 = 30°

So,

x= 90-y = 90-30 = 60°

So, value of x and y are 60° and 30° respectively