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## Step 1: Write down the given equation The given equation is: (Cos ฮธ - sin ฮธ) / (Cos ฮธ + sin ฮธ) = (1 - โ3) / (1 + โ3) ## Step 2: Cross multiply Cross multiplying the given equation: (Cos ฮธ - sin ฮธ)(1 + โ3) = (Cos ฮธ + sin ฮธ)(1 - โ3) ## 3: Expand both sides Expanding both sides: Cos ฮธ + โ3 Cos ฮธ - sin ฮธ - โ3 sin ฮธ = Cos ฮธ - โ3 Cos ฮธ + sin ฮธ - โ3 sin ฮธ ## 4: Simplify the equation Simplifying the equation: โ3 Cos ฮธ - sin ฮธ = - โ3 Cos ฮธ + sin ฮธ ## 5: Collect like terms Collecting like terms: โ3 Cos ฮธ + โ3 Cos ฮธ = sin ฮธ + sin ฮธ 2โ3 Cos ฮธ = 2 sin ฮธ ## 6: Divide by 2 Dividing by 2: โ3 Cos ฮธ = sin ฮธ ## 7: Divide by Cos ฮธ Dividing by Cos ฮธ: โ3 = tan ฮธ ## 8: Find the angle Finding the angle: ฮธ = arctan(โ3) ## 9: Recall trigonometric values Recalling trigonometric values: We know that tan(60ยฐ) = โ3 ## 10: Determine the angle Determining the angle: ฮธ = 60ยฐ ## 11: Ensure it's an acute angle Ensuring it's an acute angle: Since 60ยฐ is less than 90ยฐ, it is an acute angle. The acute angle ฮธ is 60ยฐ.Anita Singh๐ 1 karmaJul 22, 2025@Maths aiThis tool is best.
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