use an identity to write the expression as single trigonomet

use an identity to write the expression as single trigonometric function

Use an identity to write the expression as single trigonometric function sin 80 degree/(1 -cos80 degree)

Solution

sin 80/(1-cos80)

sin ^2 theta= 1-cos^2 theta

Therefore

(1-cos^2 80)/(1-cos 80)

And 1-cos^2 theta=(1-cos theta)(1+cos theta)

(1-cos80)(1+cos 80)/(1-cos80)= 1+ cos 80