How do you verify the identity #tan(pi/2-theta)tantheta=1#?

1 Answer
Jan 21, 2017

see explanation.

Explanation:

Expand the left side using the #color(blue)"trigonometric identities"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(tan(pi/2-theta)=cottheta)color(white)(2/2)|)))#

and

#color(red)(bar(ul(|color(white)(2/2)color(black)(cottheta=(costheta)/(sintheta),tantheta=(sintheta)/(costheta))color(white)(2/2)|)))#

#rArrcolor(red)cancel(costheta)/color(blue)cancel(sintheta)xxcolor(blue)cancel(sintheta)/color(red)cancel(costheta)=1=" right side"#