Solve the equation for the possible values of θ if .(tanθ - ) (sinθ - 1) = 060°90°240°300°120°NEXT QUESTION
Question
Solve the equation for the possible values of θ if .(tanθ - ) (sinθ - 1) = 060°90°240°300°120°NEXT QUESTION
Solution
To solve the equation (tanθ - ) (sinθ - 1) = 060°90°240°300°120°, we can follow these steps:
Step 1: Expand the equation: tanθ * sinθ - tanθ - sinθ + 1 = 0
Step 2: Rearrange the equation: tanθ * sinθ - sinθ - tanθ + 1 = 0
Step 3: Factor out sinθ and tanθ: sinθ(tanθ - 1) - (tanθ - 1) = 0
Step 4: Combine like terms: (tanθ - 1)(sinθ - 1) = 0
Step 5: Set each factor equal to zero and solve for θ: tanθ - 1 = 0 or sinθ - 1 = 0
For tanθ - 1 = 0: tanθ = 1 θ = arctan(1) θ = 45° + n * 180°, where n is an integer
For sinθ - 1 = 0: sinθ = 1 θ = arcsin(1) θ = 90° + n * 180°, where n is an integer
Therefore, the possible values of θ are: θ = 45° + n * 180°, where n is an integer θ = 90° + n * 180°, where n is an integer
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