Question

simplify sqrt(2tan^2theta + 4)

the answer is 2|sectheta|

i dont know how to get that answer ='[

Answer 1

This?\[\sqrt{2\tan^{2}\theta +4}\]

Answer 2

yes =]

Answer 3

I'm not sure how they got that. If you plot the original function and the answer, the curves are similar but they're not the same: http://www.wolframalpha.com/input/?i=plot+2abs%28secx%29+and+sqrt%282tan^2x%2B4%29

Are you sure you copied the problem and answer correctly?

Answer 4

Simplify the expression \[\sqrt{x ^{2}+4}\] as much as possible after substituting 2 tan 0 for x.

Answer 5

oh xD i wrote it wrong

Answer 6

on the first one

Answer 7

Lol no worries. Did you figure it out then?

Answer 8

actually no xD i still dont know how haha

Answer 9

When you substitute x with 2tan theta, you have to square the 2 also, so the problem becomes \[\sqrt{4\tan^{2}\theta +4}\]\[\sqrt{4(\tan^{2}\theta+1)} = \sqrt{4}\sqrt{\tan^{2}\theta + 1}\]Using the pythagorean identity tan^2 + 1 = sec^2, substitute tan^2 + 1\[2\sqrt{\sec^{2}\theta} = 2|\sec \theta|\]

Answer 10

I believe the question suppose
Yep!

Answer 11

@Alex I'd like to explain like that , but I'm too slow in typing!

Answer 12

ty =]

Answer 13

@marlene Directrix is extremely devoted solver, If you really want to learn, it neccessarily to have the original question so we won't misguide you!