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June Reynolds
Mathematics
30 March, 01:24
Find value of "x"
Sin (7x-20°) = Cos (3x+40°)
+4
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1
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Bradley Cole
30 March, 01:36
0
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°
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