<s>[INST] Is the substitution of standard angles while proving the equality of trigonometric formulas allowed? Here is a problem that my class 10 maths teacher gave me:

Prove that $\sec^4\theta$ - $\sec^2\theta$ = $\tan^4\theta$ + $\tan^2\theta$

She expected me to use trigonometric identities to prove such equality, but I instead substituted $\theta$ with standard angles, and substituted that with their values.
Here's what I did:

$\sec^4\theta -\sec^2\theta = \tan^4\theta + \tan^2\theta$  take $\theta$ as $45^o$  $\sec^4 45^o - \sec^2 45^o =\tan^4 45^o + \tan^2 45^o$  $(\sqrt2)^4 - (\sqrt2)^2 = (1)^4 +(1)^2$  $4 - 2 = 1+1$  $2 = 2$  therefore LHS = RHS Reason: Standard angles are universal truths, henceforth they work throughout the universe. Also, the functions used require a parameter (although not required in proving this using identities), so I substituted them all with $45^o$.

So, my question is 'Is it okay if I substitute standard angle values for trigonometric functions while proving their equality?'.
 [/INST] LHS:
$$
\sec^4\theta - \sec^2\theta = \sec^2\theta(\sec^2\theta - 1) = \frac{1}{\cos^2\theta}\frac{1-\cos^2\theta}{\cos^2\theta}=\frac{\sin^2\theta}{\cos^4\theta}
$$
RHS:
$$
\tan^4\theta + \tan^2\theta = \tan^2\theta (1 + \tan^2\theta) = \frac{\sin^2\theta}{\cos^2\theta}\frac{\sin^2\theta + \cos^2\theta}{\cos^2\theta}=\frac{\sin^2\theta}{\cos^4\theta}
$$
It's all.
</s>