If $\cos(3x - 10)° = \sin(x + 20)°$, find the value of x.
A20CORRECT
B25
C30
D15
GCEMathematicsTrigonometry2021
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Why the answer is A, and why the others tempt you.
Since cos α = sin(90° - α), we have cos(3x - 10)° = sin(90° - (3x - 10))° = sin(100 - 3x)°. Setting this equal to sin(x + 20)°: 100 - 3x = x + 20, which gives 80 = 4x, so x = 20. Substituting back: cos(50°) = sin(40°), which is true since 50° + 40° = 90°.
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