Trigonometric identities: Part III

[size=150][b]Recall the sum-to-product, product to sum, and half-angle identities. Give all common variations.[br][br][/b]Whilst you are learning the identities, write the full equation for the identity.[/size][br][br][i][color=#5b0f00][b]Example:[/b][/color][br][br][/i][b]Question:[/b][br] Reciprocal identity:[br] [math]\sin\left(x\right)=[/math][br][br][b]Answer:[/b][br] [math]\sin\left(x\right)=\frac{1}{\csc\left(x\right)}[/math]
Sum to Product[br][math]\sin\left(x\right)+\sin\left(y\right)=[/math]
Sum to Product[br][math]\cos\left(x\right)+\cos\left(y\right)=[/math]
Sum to Product[br][math]\tan\left(x\right)+\tan\left(y\right)=[/math]
Sum to Product[br][math]\sin\left(x\right)-\sin\left(y\right)=[/math]
Sum to Product[br][math]\cos\left(x\right)-\cos\left(y\right)=[/math]
Sum to Product[br][math]\tan\left(x\right)-\tan\left(y\right)=[/math]
Product to Sum[br][math]\sin\left(x\right)\sin\left(y\right)=[/math]
Product to Sum[br][math]\cos\left(x\right)\cos\left(y\right)=[/math]
Product to Sum[br][math]\sin\left(x\right)\cos\left(y\right)=[/math]
Half-angle[br][math]\sin^2\left(\frac{x}{2}\right)=[/math]
Half-angle[br][math]\cos^2\left(\frac{x}{2}\right)=[/math]
Half-angle[br][math]\tan^2\left(\frac{x}{2}\right)=[/math]
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– Stephanie Kong

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