Simplify (COS ^ 2 α - Sin ^ 2 β) / (sin ^ 2 α * sin ^ 2 β) - cot ^ 2 α cot ^ 2 β

Simplify (COS ^ 2 α - Sin ^ 2 β) / (sin ^ 2 α * sin ^ 2 β) - cot ^ 2 α cot ^ 2 β

[(COS ^ 2a-sin ^ 2b) / (sin ^ 2A * cos ^ 2b)] - cot ^ 2A * cot ^ 2b is substituted into the following formula cos2a = (COSA) ^ 2 - (Sina) ^ 2 = 2 (COSA) ^ 2 - 1 = 1-2 (Sina) ^ 2cos2a = (COSA) ^ 2 - (Sina) ^ 2sin2a = 2sina * Cosa tan2a = 2tana / [1 - (Tana) ^ 2]