How to solve pythagreom identities

Question

(1+tan^(2)x)/csc^(2)x

 

Answer 1

Hi Tyler,

 

How to solve Pythagorean identities
(1+tan²x)/csc² x

 

 

The Pythagorean Theorem is:

sin² x +cos² x =1

 

If you divide each term by cos you get:

 

tan² x +1 = sec² x

 

 

For your problem

(1+tan²x)/csc² x =

 

sec² x/csc² x =         sec² x = 1/cos² x   and csc² x = 1/sin² x

 

(1/cos² x)/(1/sin² x)=      When dividing by two fractions, take the numerator and

                                      multiply by the reciprocal of the the fraction in the denominator.

 

sin² x/cos² x =               

 

tan² x

 

 

ANSWER:   tan² x

 

It helps to write down all the identities and then refer to them when doing these types of problems.

 

hope this helps your understanding...