Rewrite each equation below. Then solve your new equation. Be sure to check your solution using the original equation.
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Since and
, we can rewrite the right side of the equation as
Using the identity , we can subtract
from either side to obtain the identity
substituting that into our previous expression, the right side of our equation simply becomes
We can now write our whole equation as
Adding 2 to both sides:
dividing both sides by 3:
When 0 ≤ x ≤ π, tan x can only be equal to 1 when sin x = cos x, which happens at x = π/4, and it can only be equal to -1 when -sin x = cos x, which happens at x = 3π/4