For I: sin2θ=((x+y)2)∕(4xy) Since x,y>0 and x≠y,(x+y)2>4xy⇒((x+y)2)∕(4xy)>1 But sin2θ≤1 always. Hence equation I is not possible. For II: sinθ+cosθ=x+1∕x By AM-GM inequality, x+1∕x≥2 for x>0 Also, |sinθ+cosθ|≤√2≈1.414 So x+1∕x≥2>√2⇒ equation II is also not possible.
