Math Question?

Question

Using the Pythagorean Identities,

What is sec^2x + csc^2x

^2=to the 2nd power

thanks!

Answer 1

This equals

1 / sin^2 x+ 1/ cos^2 x
= (sin^2 x + cos^ x ) / (sin^2 x cos^2 x) [Find a common denominator]
= 1 / (sin^2 x cos^2 x)
= 1 / (1/4 * (2sin x cos x)^2) = 4 / sin^2 2x = 4 csc^2 2x

preious answer said csc^2 x = 1 - sec^2 x. This is wrong. That equation is sin^2 x = 1 - cos^2 x. csc^2 x = 1 - sec^2 x is not a true statement

Answer 2

(sec x)^2 + (csc x) ^2 = 1 + (tan x) ^2 + 1 + (cot x) ^2 = 2 + (tan x)^2 + (cot x)^2

I am not sure what the = to the second power means

Answer 3

1/cos^2x + 1/sin^2x

=(cos^2x + sin^2x)/(sinxcosx)^2
=1/ (1/2 * sin2x)^2