Exercise 50 Page 917

We will start by rewriting the equation so that all the terms are on one side.Next, we can factor the equation and use the Zero Product Property.

Rearrange the equation and factor out common factors. Then use the Zero Product Property.

tan θ sin θ = 3 sin θ

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Simplify

$LHS - 3 sin θ = RHS - 3 sin θ$

tan θ sin θ - 3 sin θ = 0

Factor out $sin θ$

(tan θ - 3) sin θ = 0

Use the Zero Product Property

tan θ - 3 = 0 sin θ = 0 (I) (II)

$(I):$ $LHS + 3 = RHS + 3$

tan θ = 3 sin θ = 0

Let's solve these equations one at a time.

Let's isolate

θ .

tan θ = 3

$tan^{- 1} (LHS) = tan^{- 1} (RHS)$

θ = tan^{- 1} (3)