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?'.