Question 1210538
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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Would you like me to show you how to verify these solutions using their respective graphs?