Divide the equation by cos2x and create a new identity Then

Divide the equation by cos^2(x) and create a new identity. Then write that identity in two other ways. sin^2(x)+cos^2(x)=1

Solution

sin^2(x)+cos^2(x)=1

(sin^2(x)+cos^2(x))/cos^2(x)=1/cos^2(x)

(sin^2(x)/cos^2(x))+(cos^2(x)/cos^2(x))=1/cos^2(x)

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

sec^2(x)-tan^2(x)=1 is an identity

2 other ways

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

tan^2(x)=sec^2(x) -1