This is the solution by using the inequality provided; However, I seem to not understand how this $$ \begin{aligned} P & =14+5 \tan ^2 a+9 \cot ^2 a+\left(\tan ^2 b+4 \cot ^2 b\right)\left(1+\tan ^2 a\right) \\ & \geq 14+5 \tan ^2 a+9 \cot ^2 a+2 \tan b \cdot 2 \cot b\left(1+\tan ^2 a\right) \\\end{aligned} $$ was converted to this $$ \begin{aligned} & =18+9\left(\tan ^2 a+\cot ^2 a\right) \geq 18+9 \cdot 2 \tan a \cot a=36 . \\\end{aligned}$$
I understand how the inquality on the bottom is equal to 36 but I do not understand how they converted all the trigonometric function with b's to a's , or rather, evaluated them.