Question

1] 2 cos (3x - 15) = 1               [find the value of x]
2]  3 tan square (2x - 20) = 1     [find the value of x]
3]  cos square 30 + cos square x = 1        [find the value of x]

Answer 1

1)

2 cos (3x - 15 ) = 1 
cos (3x -15) = 1/2  = cos 60 = cos 300

3x - 15 = 60      or     3x - 15  = 300 

x = 75 /3      or        x = 315/3

x = 25°       or   x = 105°
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2)

3 tan² (2x-20) = 1
tan² (2x-20) = 1/3
tan (2x-20) = 1/√3

2x - 20 = 30°     or      2x-20 = 210°

x = 25°    or   x = 115°
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3)
 
  cos² 30°  + cos² x = 1 
  (√3/2)² + cos² x = 1
  cos² x = 1 - 3/4 = 1/4
  cos x = +- 1/2 
  x = 60° or 120°  or  300°   or  240°