Answer:
x = 25°
Step-by-step explanation:
sin(40 – x) = cos(3x)
The cosine of any acute angle is equal to the sine of its complement.
sin(40 - x) = sin(90 - 3x) Take arcsin of each side
40 - x = 90 – 3x Subtract 40 from each side
-x = 50 - 3x Add 3x to each side
2x = 50 Divide each side by 2
x = 25
Check:
sin(40 – 25) = cos(3 × 25)
sin(15) = cos(75)
0.2588 = 0.2588
