Solve Trigonometry equations with cos (x + α) - cos (x - α) = c and sin (x + α) - sin (x - α) = c

To solve a form equation
Cos (x + α) ± cos (x – α) = c dan sin (x + α) ± sin (x – α) = c
You can use the sine and cosine multiplication formula that we have learned in school, namely:
2 sin α cos β = sin (α + β) + sin (α - β)
2 cos α sin β = sin (α + β) - sin (α - β)
2 cos α cos β = cos (α + β) + cos (α + β)
- 2 sin α sin β = cos (α + β) - cos (α - β)

Example 1.
Determine the set of completion equations Sin (x + 210)0 + sin (x – 210)0=1/2√3 , for 0 ≤ x ≤ 360.

Answers:


X = - 30 + k . 360 or x = (180 – (- 30)) + k . 360 = 210 + k . 360, k is an integer. For intervals 0 ≤ x ≤ 360, then by choosing the appropriate k obtained x = 210 or x = 330.
So, the settlement set is {210, 330}.

Example 2.
Determine the set of resolutions from the equation Sin (x + 135)0 – sin (x – 135)0 = 1, for 0 ≤ x ≤ 360.
Answers:

x = 45 + k. 360 or x = -45 + k. 360, k are integers. So the solution is {45, 315}

Example 3
Determine the set of resolutions from the equation,


X = 5/4 π + k . 2 π  or x = (π – 5/4 π) + k . 2 π = ½ π + k . 2 π, k are integers. For intervals of 0 ≤ x ≤ 360, then selecting k accordingly is obtained x = 5/4 π or 7/4 π. So, the solution is {5/4 π, 7/4 π}.

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