20 cos theta -20 sin theta=0 then find the value of sec theta n sin theta?? plzz i need the solution of this sum

1 Answer
Apr 5, 2018

#t = (3pi)/4 + 2kpi#
#t = (7pi)/4 + 2kpi#

Explanation:

20cos t - 20sin t = 0
cos t - sin t = 0
Use the trig identity:
#sin t - cos t = sqrt2cos (t - pi/4)#
In this case:
#cos t - sin t = - sqrt2cos (t - pi/4) = 0#
#cos (t - pi/4) = 0#
Unit circle gives 2 solutions:
a. #t - pi/4 = pi/2 + 2kpi# -->
#t = pi/2 + pi/4 = (3pi)/4 + 2kpi#
b. #t - pi/4 = (3pi)/2 + 2kpi#
#t = (3pi)/2 + pi/4 = (7pi)/4 + 2kpi#