Solve and state the correct answer for the trigonometric equation below tan y = 6 - 4 cot y where

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/xx² = 6x - 4x² - 6x + 4 = 0x² - 6x + 9 = 5(x - 3)² = 5x - 3 = ± √5x = 3 + √5x = 3 - √5

Replace x with tan y:

tan y = 3 + √5 ⇒ y = arctan (3 + √5) ≈ 79.2° + 180°ktan 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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