$$1+\sec ^2 x \sin ^2 x=$$

If the identity $$\cos ^4 \theta=a \cos 4 \theta+b \cos 2 \theta+c$$ holds for some $$a, b, c \in Q$$ then $$(a, b, c)=$$

The value of $$\frac{\sin \theta+\sin 3 \theta}{\cos \theta+\cos 3 \theta}$$ is

If $$(1+\tan 1^{\circ})(1+\tan 2^{\circ}) \ldots(1+\tan 45^{\circ})=2^n,$$ then $$n=$$