if sec theta*sin(36° + theta )=0 , find the value of theta so that theta and 36°+theta are acute angles

1 answer

secØ sin(36+Ø) = 0
secØ = 0 or sin(36°+Ø) = 0
secØ can never be zero, secØ?1 OR secØ ? -1

so:
sin(36°+Ø) = 0
36+Ø = 0° or 180° or 360° or -180° ...

then Ø = -36° ,
Ø = 144° or Ø = 324

since an "acute angle" is defined as an angle between 0° < Ø < 90°
there is no solution to your question.

see Wolfram:
http://www.wolframalpha.com/input/?i=solve+secx+sin(.6283%2Bx)+%3D+0

I changed your variable to x and changed 36° to radians.