=2 Formula Used: Cosec2θ−1=cot2θ Calculation: We have
cosθ
cosecθ+1
+
cosθ
cosecθ−1
=2 ⇒
cosθ(cosecθ−1)+cosθ(cosecθ+1)
cosec2θ−1
=2 ⇒
cosθcosecθ−cosθ+cosθcosecθ+cosθ
cot2θ
=2 ⇒
2cosθcosecθ
cot2θ
=2 ⇒cosθ×(1∕sinθ)=cot2θ ⇒cotθ=cot2θ ⇒cotθ=1 ⇒θ=45∘ Now, We have to find the value of sin4θ+cos4θ Putting θ=45∘, we get ⇒sin445∘+cos445∘ ⇒(1∕4)+(1∕4)=1∕2 ∴ The value of sin4θ+cos4θ is 1∕2.