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):
$-( \frac{sin ^{2}x }{cos ^{2} x} )+( \frac{1}{cos ^{2}x } )=1$
The next step is this:
$\frac{1-sin ^{2} x}{cos ^{2}x } =1$
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:
$\frac{cos ^{2}x }{cos ^{2}x } =1$ which it does, right?