Question

Q5 Q11.) Use an identity to find the value of the expression.

Answer 1

sec^2(x) = 1 / cos^2(x)
tan^2(x) = sin^2(x) / cos^2(x)

so sec^2(x) - tan^2(x)
= 1 / cos^2(x) - sin^2(x) / cos^2(x)
= (1 - sin^2(x)) / cos^2(x)
using cos^2(x) + sin^2(x) = 1 so 1 - sin^2(x) = cos^2(x), u have
= cos^2(x) / cos^2(x)

so sec^2(102deg) - tan^2(102deg)
= cos^2(102deg) / cos^2(102deg)
= 1

Answer 2

using sec^2$\theta$ = 1 + tan*2$\theta$

the expression = 1 + tan^2(102) - tan^2(102)

= 1