(tan^(2)csc^(2)-1)/(sec^(2))

Question

why cant i simplfy tan^2csc^2-1 to tan^2cot^2 ?

Answer 1

(tan²)(csc²) = (tan²)/(sin²) = (sin²)/[(cos²)(sin²)] = 1/(cos²) = sec² 

 

sec² - 1 = tan²

 

but (tan²)(cot²) = ( tan² / tan² ) = 1

Answer 2

Because the -1 is a separate term. If it were tan²(cos² - 1), you could.

 

Just like 5(5) - 1 is not 5(4).