Question

How do you prove `sec(2x)= ((secx)^2)/(2-(secx)^2)`?

Answer 1

Prove trig expression

Explanation:

Apply the trig identities:
`sìn^2 x + cos ^2 x = 1`
`cos 2x = 2cos^2 x - 1`
`sec(2x) = 1/cos (2x) = 1/(2cos^2 x - 1)`
Divide both numerator and denominator by `cos^2 x`, we get:
`sec 2x = (1/cos^2 x)/(2 - 1/cos^2 x) = sec^2 x/(2 - sec^2 x)`