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 .