Write the first trigonometric expression in terms of the second expression. write your answer as a single fraction. sec(𝑥);cot(𝑥)

Answer 1

sin^2x + cos^2x= 1 divide both sides by cos^2x

sin^2x/cos^2x + cos^2x/cos^2x = 1/cos^2x

tan^2x + 1 = sec^2x

sec^2x = 1/cot^2x + 1

secx = + or - sqr(1/cot^2x +1)

or

sec^2x = (1+cot^2x)/cot^2x

secx = + sqr[(1+cot^2x)]/cotxor

or

secx = cscx/cotx

secx = `1/cosx, cosx = cotxsinx cosx = a/h =adjacent side over hypotenuse, cotx=a/o sinx = o/h.

a/h = a/o times o/h = (a/o)(o/h)=a/h = cotxsinx

secx =1/cotxsinx = csx/cotx since 1/sinx = cscx

secx =cscx/cotx