\(\cfrac{1-sin^2 30°}{1+sin^2 45°} \) \(\times \cfrac{cos^2 60° + cos^2 30°}{cosec^2 90 -cot^2 90°} \) \(\div (sin 60° tan 30°)\)
\(\cfrac{1-sin^2 30°}{1+sin^2 45°} × \cfrac{cos^2 60°+cos^2 30°}{cosec^2 90°-cot^2 90°}\)
\( ÷(sin 60°.tan 30°)\)
\(=\cfrac{1-(\cfrac{1}{2})^2}{1+(\cfrac{1}{√2})^2} ×\cfrac{(\cfrac{1}{2})^2+(\cfrac{√3}{2})^2}{(1)^2-(0)^2}÷(\cfrac{√3}{2}×\cfrac{1}{√3})\)
\(=\cfrac{1-\cfrac{1}{4}}{1+\cfrac{1}{2}}×\cfrac{\cfrac{1}{4}+\cfrac{3}{4}}{1-0}÷\cfrac{1}{2}\)
\(=\cfrac{\cfrac{3}{4}}{\cfrac{3}{2}}×1 \times \cfrac{2}{1}\)
\(=\cfrac{3}{4}×\cfrac{2}{3}×2\)
\(=1\) (Answer)