UPSC CDS 1 2022 Math Paper

Shortcut Trick
Given cos‌θ+sec‌θ−2=0
⇒cos‌θ+1∕cos‌θ−2=0
We know that the maximum value of cos‌θ=1 at θ=0∘
So, the above equation is valid only when θ=0∘

Now we have to find cos4θ+sec4θ−2
At θ=0∘
cos40∘+sec40∘−2
⇒1+1−2=0
∴ The required value of cos4θ+sec4θ−2 is 0 .