Find value of "x"

Sin (7x-20°) = Cos (3x+40°)

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°