compound angles question

1.solve (sin x+ cos x )^2 = 2sin(π/4+x)sin(π/4-x)
for 2π≧x≧0

2.in ⊿ABC
a) show that sin A=sin(B+C)
b) suppose that tan B= cos(B-C)/(sinA-sin(B-C))
i)show that cos B cos (B+C)= 0
ii)hence , prove that A=π/2

3.given cos(θ+α)=p and sin(θ+β)=q
a)express cosθ and sinθ in terms of α, β, p, q
b)hence, show that p^2+q^2+2pq sin(α-β)=cos^2(α-β)