Question

sin^2(pie/4-x)+sin^2(pie/4+x)=1

Answer 1

LHS

=sin

2

(

4

π

−x)+sin

2

(

4

π

+x)

=[sin(

4

π

−x)]

2

+[sin(

4

π

+x)]

2

=[sin

4

π

cosx−cos

4

π

sinx]

2

+[sin

4

π

cosx+cos

4

π

sinx]

2

=(sin

4

π

cosx)

2

+(cos

4

π

sinx)

2

+(sin

4

π

cosx)

2

+(cos

4

π

sinx)

2

=2(sin

4

π

cosx)

2

+2(cos

4

π

sinx)

2

=2(

2

1

cosx)

2

+2(

2

1

sinx)

2

=1

=RHS