SOLUTION: Find the values of x in the range 0°≤x≤360°, which satisfy the equation below
i) sin3xsinx = 2cos2x + 1
ii) 3cotx + tanx - 4 = 0
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-> SOLUTION: Find the values of x in the range 0°≤x≤360°, which satisfy the equation below
i) sin3xsinx = 2cos2x + 1
ii) 3cotx + tanx - 4 = 0
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You can put this solution on YOUR website! To solve these trigonometric equations, we will use fundamental identities to simplify them into a solvable form.
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## i)
To solve this, we can use the **Product-to-Sum formula**:
**Step 1: Apply the formula to the left side.**
Let and :
**Step 2: Simplify and rearrange.**
Multiply the entire equation by :
**Step 3: Use the Double Angle formula for .**
Recall that . Here, let :
**Step 4: Factor the quadratic.**
Let :
So, or .
**Step 5: Solve for in the range .**
Since , then .
* **Case 1: **
* **Case 2: **
**Solution (i):**
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## ii)
**Step 1: Rewrite in terms of .**
Since , the equation becomes:
**Step 2: Form a quadratic equation.**
Multiply through by (noting that ):
**Step 3: Factor the quadratic.**
So, or .
**Step 4: Solve for in the range .**
* **Case 1: **
* **Case 2: **
**Solution (ii):**
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