Trig: Product-to-Sum and Sum-to-Product Identities
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Problems 14
- Rewrite the product as a sum. 16sin(16x)sin(11x)\\16\sin(16x)\sin(11x)16sin(16x)sin(11x)
- Rewrite the product as a sum. 20cos(36t)cos(6t)\\20\cos(36t)\cos(6t)20cos(36t)cos(6t)
- Rewrite the product as a sum. 2sin(5x)cos(3x)\\2\sin(5x)\cos(3x)2sin(5x)cos(3x)
- Rewrite the product as a sum. 10cos(5x)sin(10x)\\10\cos(5x)\sin(10x)10cos(5x)sin(10x)
- Rewrite the product as a sum. cos(6t)+cos(4t)\\\cos(6t)+\cos(4t)cos(6t)+cos(4t)
- Rewrite the product as a sum. cos(6u)+cos(4u)\\\cos(6u)+\cos(4u)cos(6u)+cos(4u)
- Rewrite the product as a sum. sin(3x)+sin(7x)\\\sin(3x)+\sin(7x)sin(3x)+sin(7x)
- Rewrite the sum as a product. sin(h)+sin(3h)\\\sin(h)+\sin(3h)sin(h)+sin(3h)
- Solve for all solutions. cos(5x)=−cos(2x)\\\cos(5x)=-\cos(2x)cos(5x)=−cos(2x)
- Solve for all solutions. sin(5x)=sin(3x)\\\sin(5x)=\sin(3x)sin(5x)=sin(3x)
- Solve for all solutions. cos(6θ)−cos(2θ)=sin(4θ)\\\cos(6\theta)-\cos(2\theta)=\sin(4\theta)cos(6θ)−cos(2θ)=sin(4θ)
- Solve for all solutions. cos(8θ)−cos(2θ)=sin(5θ)\\\cos(8\theta)-\cos(2\theta)=\sin(5\theta)cos(8θ)−cos(2θ)=sin(5θ)
- Simplify, sin(7t)+sin(5t)cos(7t)+cos(5t)\dfrac{\sin(7t)+\sin(5t)}{\cos(7t)+\cos(5t)}cos(7t)+cos(5t)sin(7t)+sin(5t)
- Simplify, sin(9t)−sin(3t)cos(9t)+cos(3t)\dfrac{\sin(9t)-\sin(3t)}{\cos(9t)+\cos(3t)}cos(9t)+cos(3t)sin(9t)−sin(3t)