Given expression: 1+2sin2θcos2θ−sin4θ−cos4θ Where, 0∘<θ<90∘ ⇒1+2sin2θcos2θ−sin4θ−cos4θ =1−[sin4θ+cos4θ −2sin2θcos2θ] =1−[(sin2θ)2+(cos2θ)2 −2sin2θ⋅cos2θ] =1−[(cos2θ−sin2θ)2] [∵a2+b2−2ab=(a−b)2] =1−[(cos2θ)2] [∵cos2x=cos2x−sin2x] =1−cos22θ=sin22θ [∵sin2A+cos2A=1] For maximum value sin22θ=1 ⇒sin2θ=1⇒2θ=90∘ ⇒θ=45∘ ∴ Maximum value =1+2sin245∘cos245∘−sin445∘−cos445∘ =1+2⋅