Answer:
Because the actual identity says [tex]\sin ^{2}\theta +\cos ^{2}\theta = 1[/tex]
Step-by-step explanation:
The trigonometric ratios [tex]\sin \theta[/tex] and [tex]\cos\theta[/tex] have a maximum value of 1. And hence [tex]\cos^{2}\theta[/tex] and [tex]\sin^{2}\theta[/tex] will have values between 0 and 1 as they are squares and will be always positive.
But if we look at the equation [tex]\cos^{2}\theta-\sin^{2}\theta=1[/tex] shows that [tex]\cos^{2}\theta[/tex] will be more than 1. Hence it is an incorrect equation.
The correct relation between [tex]\cos^{2}\theta[/tex] and [tex]\sin^{2}\theta[/tex] is [tex]\sin ^{2}\theta +\cos ^{2}\theta = 1[/tex].
