SOLUTION: Find the values of x in the range 0°≤x≤360°, which satisfy the equation below i) sin3xsinx = 2cos2x + 1 ii) 3cotx + tanx

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

Question 1210538: 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

Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(2189) (Show Source): 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):**
---
## 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):**
---
Would you like me to show you how to verify these solutions using their respective graphs?
Answer by ikleyn(53575) (Show Source): You can put this solution on YOUR website!
.

Dear @CPhill,

Your posts are doing more harm than good to students' learning.

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