Answer:
x = 36°n + 7° OR x = 90°n + 37.5° for any integer n
Step-by-step explanation:
Since cos(x) = sin(90°-x), we have
sin(7x-20°) = sin(90°-(3x+40°)) = sin( 50° - 3x )
sin( x ) = sin( y ) implies either:
x = 360° n + y
or
x = 360°n + 180° - y
Generally sin(x) = sin(y) ⇒ x = 180°n + (-1)ⁿ y
First case:
7x - 20° = 360°n + 50° - 3x
10x = 360°n + 70°
x = 36°n + 7°
Second case:
7x - 20° = 360°n + 180° - ( 50°-3x )
7x - 20° = 360°n + 180° - 50° + 3x
7x - 20° = 360°n + 130° + 3x
4x - 20° = 360°n + 130°
4x = 360°n + 150°
x = 90°n + 37.5°
