Question

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

Answer 1

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"`