anonymous one year ago is cos^2x(1+tan^2x)=1 an identity? explain your reasoning.

1. johnweldon1993

I would say so $\large cos^2(x)(1 + tan^2(x)) = 1$ What is $$\large 1 + tan^2(x)$$ ?

2. anonymous

$\sec^2 x$

3. johnweldon1993

Right...so $\large cos^2(x)sec^2(x) = 1$ Now...we know $$\large sec^2(x)$$ can be written as $$\large \frac{1}{cos^2(x)}$$ So $\large cos^2(x)(\frac{1}{cos^2(x)}) = 1$ $\large \frac{cos^2(x)}{cos^2(x)} = 1$ Is that a true statement?

4. anonymous

yes, thank you!