Question

I need help figuring Identities....

cosx(tan^2x+1) = secx

Answer 1

\(\bf {\color{brown}{ 1+tan^2(\theta)=sec^2(\theta)}}\quad thus
\\ \quad \\
cos(x)[tan^2(x)+1]\implies ?\)

Answer 2

thats where i'm having a problem with while i'm solving it....

Answer 3

well... what would that give you anyway?

keep in mind secant = 1/cosine

Answer 4

i dont know about the cosine but i do know whats in the parenthesis. cosx(sec^2x)

Answer 5

yeap thus

Answer 6

I usually change everything to sin and cos and see if things simplify

Answer 7

\(\bf {\color{brown}{ 1+tan^2(\theta)=sec^2(\theta)}}\quad thus
\\ \quad \\
cos(x)[tan^2(x)+1]\implies cos(x)sec^2(x)\implies \cancel{ cos(x) }\cfrac{1}{\cancel{ cos^2(x) }}\)

yeap... that'd work too

Answer 8

thus . . . . i dont know what to do after that.

Answer 9

http://www.mathwords.com/t/trig_identities.htm check what 1/cos(x) is then

Answer 10

its secx. but how can i just get sex by itself. do i just cancel or something.

Answer 11

secx*

Answer 12

That's what he did in the last step.
\(\large cos(x)*sec^2(x)=\cancel{cos(x)}*\frac{1}{cos^\cancel{2}(x)}=\frac{1}{cosx}=secx\)

Answer 13

\(\large \frac{a^m}{a^n}=a^{m-n}\)

Answer 14

Ah ok. Thanks