Show that none of the following is an identity:
tan2 θ + sin θ = cos2 θ
If the given equation is an identity, then it is true for every value of θ.
So, let θ = 30°
So, for θ = 30°, consider the L.H.S. = tan2 30° + sin 30°
= (1/√3)2 + (1/2)
= (1/3) + (1/2)
= 5/6
Consider the R.H.S. = cos2 30° = (√3/2)2
= 3/4
Therefore, L.H.S. ≠ R.H.S.
Thus, the given equation is not an identity.