Use the Pythagorean identities to write the expression as an

Use the Pythagorean identities to write the expression as an integer. tan^2 4beta - sec^2 4beta Simplify the expression.

Solution

tan^2 (4beta) -sec^2 (4beta)=

By identity we know that sec^2(beta)=1+tan^2 (beta) equation 1

tan^2(4beta)-sec^2 (4beta)=tan^2(4beta)-tan^2(4beta)-1=-1

b) 4tan^2 (beta)-4sec^2 (beta)=4(tan^2(beta)-sec^2 (beta))

=4(tan^2 (beta)-tan^2 (beta)-1)=4(-1)=-4

By using above identity in equation 1