Question

I'm having trouble verifying this identity. - tan^2x + sec^2x = 1

Answer 1

tan^2 + 1 = sec^2x

Answer 2

?

Answer 3

wouldn't it be -tan^2(x) + sec^2(x) = 1?

Answer 4

so if you subtract tan^2x from both sides what do you get?

Answer 5

We know that tan^2x + 1 = sec^2x

Answer 6

but that isn't verifying if i subtract sec^2(x)?

Answer 7

-tan^2(x) + sec^2(x)
-(sin(x)/cos(x))^2 + 1/cos^2(x)
1/cos^2(x) (-sin^2(x) + 1))
1/cos^2(x)(cos^2(x)) = 1
is this correct?

Answer 8

\(\large\tt \begin{align} \color{black}{- tan^2x + sec^2x = 1\\
-\dfrac{sin^2x}{cos^2x}+\dfrac{1}{cos^2x}\\~\\\
=\dfrac{-sin^2x+1}{cos^2x}\\~\\
=\dfrac{cos^2x}{cos^2x}\\
=1
}\end{align}\)