Question

Please help...
Verify the identities of these trig equations
-tan^2x +sec^2x = 1

Answer 1

The first step in simplifying is this one (since tangent is sin/cos, and sec and is the same as 1/cos):

`-( (sin ^(2)x )/(cos ^(2) x) )+( (1)/(cos ^(2)x ) )=1`
The next step is this:

`(1-sin ^(2) x)/(cos ^(2)x ) =1`
Now the next step in this identity involves knowing another identity, which is this one (a Pythagorean identity, actually);

`sin ^(2) x+cos ^(2) x=1` and
`cos ^(2)x=1-sin ^(2) x`
So let's sub that in, like this:

`(cos ^(2)x )/(cos ^(2)x ) =1` which it does, right?