If sec x 8 use trigonometric identities to find the exact v

If sec x = 8, use trigonometric identities to find the exact value of tan x = _____ tan^2 x = _____ csc(pi/2 - x) = _____ sin^2 x = _____

Solution

secx = 8

cosx = 1/8

height =sqrt( 8^2 -1 ) = sqrt63 = 3sqrt7

tanx = 3sqrt(7)/1= 3sqrt(7)

tan^7(x) = 3(7)^7/2

csc(pi/2 +x) = 1/sin( pi/2 +x)

= cosx = 1/8

sin^2x = sqrt( 1- cos^2x) = sqrt(1 - 1/8^2 ) = sqrt(63/64) = 3sqrt(7)/8