Using the identity Cos(A-B) = CosA CosB + SinA SinB, observe that your equation can be rewritten by rearranging letters in the identity to Cos(40° - x) = sqrt(3)/2.
Now, using a special angles in trigonometry, the angle whose cosine equals the square root of 3 divided by 2 is 30 degrees or π/6 (in radians).
Therefore, the solutions are given by:
40° - x = 30°, which simplifies to x = 10°
AND
40° - x = 30° + 180k for any integer k.
Therefore, x = 40° - 30° + 180k = 10° + 180k for any integer k.
Solve the equation
Cos40° Cosx + sin 40° sin x=square root 3/2
1 answer
1 answer