证明:cos^4α+sin^2αcos^2α+sin^2α+tan^2α=sec^2α

问题描述:

证明:cos^4α+sin^2αcos^2α+sin^2α+tan^2α=sec^2α

cos^4α+sin^2αcos^2α+sin^2α+tan^2α
=cos^2 α(cos^2 α+sin^2 α)+sin^2α+tan^2α
=cos^2 α+sin^2α+tan^2α
=1+tan^2α
=sec^2α