SOLUTION: 1. Verify the identity. sin(9𝑥)+sin(3𝑥)/cos(9𝑥)+cos(3𝑥)=tan(6𝑥) 2. Find the exact value of the following expression given that tan𝜃 =−2 and 90°<𝜃

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Question 1187012: 1. Verify the identity.
sin(9𝑥)+sin(3𝑥)/cos(9𝑥)+cos(3𝑥)=tan(6𝑥)
2. Find the exact value of the following expression given that tan𝜃 =−2 and
90°<𝜃 <180°. Show all logic for your choices, including pictures of the quadrant to derive signs and a triangle to derive trigonometric values.

sin2𝜃

These two problems are so confusing for me. First, I'm not sure where to begin and how to solve it at all. How do I verify the identity and the second, I am really lost on what to do. Please help.
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
1. Verify the identity.
sin(9𝑥)+sin(3𝑥)/cos(9𝑥)+cos(3𝑥)=tan(6𝑥)
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Look up "Half Angle Formulas" on Wikipedia.
2. Find the exact value of the following expression given that tan𝜃 =−2 and
90°<𝜃 <180°. Show all logic for your choices, including pictures of the quadrant to derive signs and a triangle to derive trigonometric values.

sin2𝜃

These two problems are so confusing for me. First, I'm not sure where to begin and how to solve it at all. How do I verify the identity and the second, I am really lost on what to do. Please help.