Question

(cos x+ cosy) ^2 + (sin x - sin y)^2= 4 sin^2 (x-y) /2​

Answer 1

Answer:

LHS :

(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

Answer 2

Answer:

LHS:

(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+2 cos(x+y)

=2+2 cos(x+y)

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

=4 cos

2

2

x+y

) = RHS