How to simplify $(1-\tan^4θ) \cos^2θ+\tan^2θ=$?

Question

How to simplify:(change tan.cos into sec .cot or others to make this formula shorter) $$ (1-\tan^4θ)\cos^2θ+\tan^2θ=? $$

I have an answer, but I'm not sure if it is correct. $$ \begin{split} (1-\tan^4θ)\cos^2θ+\tan^2θ &=(1-\tan^2θ) (1+\tan^2θ)\cos^2θ + \tan^2θ \\ &= \sec^2θ*(1+\tan^2θ)*\cos^2θ + \tan^2θ \\ &=1+\tan^2θ+ \tan^2θ \\ &=1+2\tan^2θ \end{split} $$

Answer 1

we can express all by $\cos(x)$

$${\frac {1}{ \left( \cos \left( x \right) \right) ^{2}} \left( \left( {\frac {2\, \left( \cos \left( x \right) \right) ^{2}-1}{ \left( \cos \left( x \right) \right) ^{4}}} \right) ^{ \left( \cos \left( x \right) \right) ^{2}} \left( \cos \left( x \right) \right) ^{2}+1- \left( \cos \left( x \right) \right) ^{2} \right) } $$

Answer 2

You get $$ \begin{split} \left(1-\tan^4 x\right)\cos^2x+\tan^2 x &= \left(1-\tan^2 x\right)\left(1+\tan^2 x\right) \cos^2x+\tan^2 x \\ &= \left(1-\tan^2 x\right)\sec^2 x \cos^2x+\tan^2 x \\ &= \left(1-\tan^2 x\right) + \tan^2 x \\ &= 1. \end{split} $$