Show that none of the following is an identity:

cos2 θ + cos θ = 1

If the given equation is an identity, then it is true for every value of θ.

So, let θ = 60°


So, for θ = 60°, consider the L.H.S. = cos2 60° + cos 60°


= (1/2)2 + (1/2)


= (1/4) + (1/2)


= 3/4 1


Therefore, L.H.S. R.H.S.


Thus, the given equation is not an identity.


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