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Sagot :
Answer:
- y = {37.4°, 79.2°, 217.4°, 259.2°}
Step-by-step explanation:
Given
- tan y = 6 - 4 cot y
We now that
- cot y = 1/tan y
Substitute tan y with x:
- x = 6 - 4/x
- x² = 6x - 4
- x² - 6x + 4 = 0
- x² - 6x + 9 = 5
- (x - 3)² = 5
- x - 3 = ± √5
- x = 3 + √5
- x = 3 - √5
Replace x with tan y:
- tan y = 3 + √5 ⇒ y = arctan (3 + √5) ≈ 79.2° + 180°k
- tan y = 3 - √5 ⇒ y = arctan (3 - √5) ≈ 37.4° + 180°k
Answer is:
- y = {37.4°, 79.2°, 217.4°, 259.2°}
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