Use the fundamental identities to simplify the expression

Using sin

^{2}x+cos^{2}x=1 the above expression is 2sec^{2}x*cos^{2}x but sec(x)=1/cos(x) so we have 2*cos^{2}x/cos^{2}x=2.So this expression is just 2. and we used two fundamental identities to simplify.

Jim

## Comments

^{2}x and 2. 1-sin^{2}x let take them one at a time^{2}(x)=2/cos^{2}(x) so much for that. Now lets look at the second factor (1-sin^{2}(x)). You should know that sin^{2}(x)+cos^{2}(x)=1. This is a fundamental relationship related to the Pythagorean theorem. Using this relationship we can solve it for cos^{2}(x)=1-sin^{2}(x)^{2}(x))*(cos^{2}(x)) the cos^{2}(x) terms in the numerator and denominator cancel leaving the factor 2. Q.E.D.