Question

simplify sec^2(theta)-cos^2(theta)*sec^2(theta)

Answer 1

Keep in mind that Sec(theta) = 1/Cos(theta)

Answer 2

Which means that:
Sec^2(theta) = 1^2/Cos^2(theta) = 1/Cos^2(theta)

Answer 3

Plugging that into your equation:
1/Cos^2(theta) - Cos^2(theta) * 1/Cos^2(theta) = 1/Cos^2(theta) - 1

Answer 4

If we simplify this a bit further by finding the common denominator, we get:

[1-Cos^2(theta)]/Cos^2(theta) = Sin^2(theta)/Cos^2(theta) = Tan^2(theta)

Answer 5

Since Sin^2(theta)+Cos^2(theta)=1

Answer 6

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