How do you simplify #(1- tan^2θ) /( 1+ tan^2 θ)#?
2 Answers
Explanation:
Using the identities:
Start:
Split the numerator:
Explanation:
#"using the "color(blue)"trigonometric identities"#
#•color(white)(x)tantheta=sintheta/costheta#
#•color(white)(x)sin^2theta+cos^2theta=1#
#•color(white)(x)cos^2theta-sin^2theta=cos2theta#
#rArr(1-tan^2theta)/(1+tan^2theta)#
#=(1-sin^2theta/cos^2theta)/(1+sin^2theta/cos^2theta)xxcos^2theta/cos^2theta#
#=(cos^2theta-sin^2theta)/(cos^2theta+sin^2theta)#
#=cos^2theta-sin^2theta=cos2theta#