Question

if (sin x + sin y )= "a" and (cos x + cos y )= "b" than prove , cos (1/2) (x-y)= +_ (1/2 )√(a^ 2 +b^ 2)​

Answer 1

Answer:

Step-by-step explanation:

(cosx+cosy)

2

+(sinx−siny)

2

=(cos

2

x+cos

2

y+2cosxcosy)+(sin

2

x+sin

2

y−2sinxsiny)

=(cos

2

x+sin

2

y)+(cos

2

x+sin

2

y)+2(cosxcosy−sinxsiny)

=1+1+2cos(x+y)

=2+2cos(x+y)

=2[1+cos(x+y)]

=4 cos

2

(

2

x+y

​

) = RHS