If the solution for the trigonometric equation above is , for integers and , what is the value of ?
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we have:
∗ cos x + sin x tan 2 x = cos x + sin x ( sin x 1 − cos x ) = 1
∗ sin ( x − 3 0 ∘ ) + cos ( 6 0 ∘ − x ) = 2 3 sin x − 2 1 cos x + 2 1 cos x + 2 3 sin x = 3 sin x
Therefore our equation can be written as :
sec 2 x − 1 = cos x 3 sin x
< = > tan x ( tan x − 3 ) = 0
= > x = 1 8 0 ∘ n or x = 6 0 ∘ + 1 8 0 ∘ n = 6 0 ∘ ( 3 n + 1 ) , so a = 6 0 , b = 3 , a / b = 2 0
Note that if x is a multiple of 1 8 0 ∘ , then tan 2 x is undefined.