Question

Prove that -- sec^2ø-tan^2ø=1

Answer 1

Hello from MrBillDoesMath!

 

Answer:

See discussion below

Discussion:

sec(@) = 1/cos(@)

and

tan(@) = sin(@)/ cos(@)

so the equation in the Question is equivalent to

( 1/ (cos^2(@) )  - ( sin^2(@) / cos^2(@) )

Combine the two terms over the like denominator cos^2(@):

( 1 - sin^2(@) )   /  (cos^2(@) )

But as sin^2(@) + cos^2(@) = 1,  1 - sin^2(@) = cos^2(@). Using this the above equation becomes o

(cos^2(@))  /  ((cos^2(@))  = 1    

This proves the result.

Thank you,

MrB