Question

verify: sec^2x/tanx+cot^2xtanx =tanx

Answer 1

well start by factoring the deominator

\[\frac{\sec^2(x)}{\tan(x)(1 + \cos^2(x))} \]

Answer 2

ok then you get the bottom to be tanx (cscx)
right

Answer 3

oops should be

\[\frac{\sec^2(x)}{\tan(x)(1 + \cot^2(x)}\]

so yes you have

\[\frac{1}{\tan(x)} \times \frac{\sec^2(x)}{\csc^2(x)} = \]

so what do you think about sec^2/csc^2...?

Answer 4

\[\frac{\sec^2(x)}{\csc^2(x)} = \frac{1}{\cos^2(x)} \div \frac{1}{\sin^2(x)} = \frac{1}{\cos^2(x)} \times \frac{\sin^2(x)}{1} \]

any thoughts..?

Answer 5

then multiply the answer above by

\[\frac{1}{\tan(x)}\]

Answer 6

is that right

Answer 7

thats correct you you could have just used

\[\frac{1}{\tan(x)} \times \frac{\sin^2(x)}{\cos^2(x)} = \frac{1}{\tan(x)} \times \tan^2(x) = \tan(x)\]