UPSC CDS 1 2022 Math Paper

Shortcut Trick
Since the condition for α and β are not given
So, we can take any value of α and β
Let α=β=45∘ we can take 0∘ also but not 90∘ because tan‌90∘=∞
Now, On putting α=β=45∘ in the given equation, we get
(sec245∘+tan‌45∘⋅tan‌45∘−tan245∘)2+(tan‌45∘−tan‌45∘)2−sec245∘⋅sec245∘
⇒[(√‌2)2+1×1−1]2+(1−1)2−(√‌2)2×(√‌2)2
⇒4+0−4=0
∴ The required answer is 0 .