SOLUTION: How do I verify this identity? (tan of theta + cotangent of theta) ^2 = sec ^2 of theta + csc ^ 2 of theta if you don't mind, please help show me the steps thank you

Algebra ->  Trigonometry-basics -> SOLUTION: How do I verify this identity? (tan of theta + cotangent of theta) ^2 = sec ^2 of theta + csc ^ 2 of theta if you don't mind, please help show me the steps thank you      Log On


   

Question 916899: How do I verify this identity?
(tan of theta + cotangent of theta) ^2 = sec ^2 of theta + csc ^ 2 of theta

if you don't mind, please help show me the steps
thank you
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
ow do I verify this identity?
(tan of theta + cotangent of theta) ^2 = sec ^2 of theta + csc ^ 2 of theta
***
use x for theta
%28tanx%2Bcotx%29%5E2=sec%5E2%28x%29%2Bcsc%5E2%28x%29
start with left side:
%28tanx%2Bcotx%29%5E2=tan%5E2%28x%29%2B2tanxcotx%2Bcot%5E2%28x%29
tanx*cot=1
using pythagorean identities:
tan^2(x)=sec^2(x)-1
cot^2(x)=csc^2(x)-1

verified: left side = right side