Question

how do you prove the following is equal? 1+cos2x/sin2x = cotx

Answer 1

TRIGONOMETRY FORMULAS TO BE USED.
# 1+cos 2x= 2 cos^2x .....(1)
# sin2x= 2sinx cosx ......(2)
LHS
(1+cos2x)/sin2x
2cos^2x/ 2sinx cosx .....[from (1) &(2)]
cosx/sinx
cotx=RHS

Answer 2

1+cos^2(x)/sin^2(x) = cotx
1+cos^2(x)/sin^2(x) = cos x/sin x

assume cosx/sinx = Y, then

1 + Y^2 = Y
Y^2 - Y + 1 = 0

Solve Y

Answer 3

use the quadratic formula