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Prove that: cos^2 x (1-sec^2 x)= -sin^2 x?
help with the steps to proving the identity
2 Answers
- ?Lv 72 years ago
cos^2(x)(1 - sec^2(x)) (left)
Distribute through.
= cos^2(x) - cos^2(x)sec^2(x)
Cosine and secant are reciprocals: they make 1.
= cos^2(x) - 1
This is a variation/rearrangement of the fundamental identity sin^2(x) + cos^2(x) = 1. Factor out a -1.
= -(1 - cos^2(x))
= -sin^2(x) (right). Done.
Not a pure identity, since cos(x) =/= 0 due to sec(x) on the left. Right side has no restrictions whatsoever.
