Question

-tan ^ 2 x+ sec ^2 x = 1

Answer 1

First change everything into sine and cosine\[\Large -\frac{ \sin^2 x }{ \cos^2 x }+ \frac{ 1 }{ \cos ^2 x }\]now you can add the fractions since they have like denominators
\[\Large \frac{- \sin^2 x +1 }{ \cos^2 x }\]maybe change the order \[\Large \frac{1- \sin^2 x }{ \cos^2 x }\]Does that top part look familiar?

Answer 2

Yeah

Answer 3

1 - sin^2 (x) = cos^2 (x) so then it would be cos^2 (x) / cos^2(x)

Answer 4

Right

Answer 5

And cos^2 x/ cos^2 x is equal to...

Answer 6

sine ?

Answer 7

No... a number divided by itself equals 1.

What then must this be equal to?
\[\Large \frac{ \cos^2 x }{ \cos^2 x }= ???\]