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Sinθ(1+tanθ)=tanθ(sinθ+cosθ)

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Answer:

To solve the equation sinθ(1+tanθ) = tanθ(sinθ+cosθ), let's simplify both sides step-by-step.

1. Expand the left side of the equation:

sinθ + sinθtanθ = tanθ(sinθ + cosθ)

2. Distribute tanθ on the right side:

sinθ + sinθtanθ = tanθsinθ + tanθcosθ

3. Move all terms to one side of the equation:

sinθ + sinθtanθ - tanθsinθ - tanθcosθ = 0

4. Factor out sinθ from the first two terms and factor out tanθ from the last two terms:

sinθ(1 + tanθ) - tanθ(sinθ + cosθ) = 0

5. Now, we can see that both sides of the equation are equal to zero:

sinθ(1 + tanθ) - tanθ(sinθ + cosθ) = 0

This equation is already simplified and cannot be further simplified.

User Priyanka Alachiya
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