Mini Tools for Maths

## Step 1: Write down the given equation The given equation is: (Cos θ - sin θ) / (Cos θ + sin θ) = (1 - √3) / (1 + √3) ## Step 2: Cross multiply Cross multiplying the given equation: (Cos θ - sin θ)(1 + √3) = (Cos θ + sin θ)(1 - √3) ## 3: Expand both sides Expanding both sides: Cos θ + √3 Cos θ - sin θ - √3 sin θ = Cos θ - √3 Cos θ + sin θ - √3 sin θ ## 4: Simplify the equation Simplifying the equation: √3 Cos θ - sin θ = - √3 Cos θ + sin θ ## 5: Collect like terms Collecting like terms: √3 Cos θ + √3 Cos θ = sin θ + sin θ 2√3 Cos θ = 2 sin θ ## 6: Divide by 2 Dividing by 2: √3 Cos θ = sin θ ## 7: Divide by Cos θ Dividing by Cos θ: √3 = tan θ ## 8: Find the angle Finding the angle: θ = arctan(√3) ## 9: Recall trigonometric values Recalling trigonometric values: We know that tan(60°) = √3 ## 10: Determine the angle Determining the angle: θ = 60° ## 11: Ensure it's an acute angle Ensuring it's an acute angle: Since 60° is less than 90°, it is an acute angle. The acute angle θ is 60°.

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