What is sec^4thetasec4θ in terms of non-exponential trigonometric functions?

1 Answer
Jun 15, 2016

=8/(3+4cos2theta+cos4theta)=83+4cos2θ+cos4θ

Explanation:

sec^4theta=1/cos^4thetasec4θ=1cos4θ

=1/(1/2(1+cos2theta))^2=1(12(1+cos2θ))2

=1/(1/4(1+2cos2theta+cos^2 2theta)=114(1+2cos2θ+cos22θ)

=4/(1+2cos2theta+1/2(1+cos4theta))=41+2cos2θ+12(1+cos4θ)

=8/(3+4cos2theta+cos4theta)=83+4cos2θ+cos4θ