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Use Product-To-Sum Formulas To Rewrite Trigonometric Functions

Use product-to-sum formulas to rewrite cosx.cosy

$\frac{1}{2}\left(\cos\cos\left(x-y\right)\right)\frac{1}{2}\left(\cos\cos\left(2x-5y\right)+\cos\cos\left(2x-5y\right)\right)$

$\frac{1}{2}\left(\cos\cos\left(x-y\right)+\cos\cos\left(x+y\right)\right)$

$\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x+5y\right)\right)$

Use product-to-sum formulas to rewrite sin6x.sin4x

$\frac{1}{2}\left(\sin\sin5x+\sin\sin x\right)$

$\frac{1}{2}\left(\sin\sin3x+\sin\sin x\right)$

$\frac{1}{2}\left(\cos\cos\left(2x\right)-\cos\cos\left(10x\right)\right)$

Use product-to-sum formulas to rewrite sin3x.sin2x

$\frac{1}{2}\left(\sin\sin5x+\sin\sin x\right)$

$\frac{1}{2}\left(\sin\sin3x+\sin\sin x\right)$

$\frac{1}{2}\left(\cos\cos\left(x\right)-\cos\cos\left(5x\right)\right)$

Use product-to-sum formulas to rewrite sin2x.cosx

$\frac{1}{2}\left(\sin\sin5x+\sin\sin x\right)$

$\frac{1}{2}\left(\sin\sin3x+\sin\sin x\right)$

$\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x+5y\right)\right)$

Use product-to-sum formulas to rewrite cosx.cos2x

$\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x-5y\right)\right)$

$\frac{1}{2}\left(\cos\cos\left(x-y\right)-\cos\cos\left(x+y\right)\right)$

$\frac{1}{2}\left(\cos\cos\left(-x\right)-\cos\cos\left(3x\right)\right)$

Use product-to-sum formulas to rewrite sin7x.sin4x

$\frac{1}{2}\left(\sin\sin5x+\sin\sin x\right)$

$\frac{1}{2}\left(\cos\cos3x-\cos\cos11x\right)$

$\frac{1}{2}\left(\cos\cos2x-\cos\cos10x\right)$

Use product-to-sum formulas to rewrite sin5x.sin2x

$\frac{1}{2}\left(\cos\cos\left(3x\right)-\cos\cos\left(7x\right)\right)$

$\frac{1}{2}\left(\sin\sin3x+\sin\sin x\right)$

$\frac{1}{2}\left(\cos\cos\left(x\right)-\cos\cos\left(5x\right)\right)$

Use product-to-sum formulas to rewrite sin4x.cos2x

$\frac{1}{2}\left(\sin\sin6x+\sin\sin2x\right)$

$\frac{1}{2}\left(\sin\sin3x+\sin\sin x\right)$

$\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x+5y\right)\right)$

Use product-to-sum formulas to rewrite sin3x.cos2x

$\frac{1}{2}\left(\sin\sin\left(5x\right)+\sin\sin\left(x\right)\right)$

$\frac{1}{2}\left(\sin\sin\left(11x\right)+\sin\sin\left(x\right)\right)$

$\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x+5y\right)\right)$

Use product-to-sum formulas to rewrite sin6x.cos5x

$\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x-5y\right)\right)$

$\frac{1}{2}\left(\sin\sin\left(11x\right)+\sin\sin\left(x\right)\right)$

$\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x+5y\right)\right)$

Questions

Time

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Use Product-To-Sum Formulas To Rewrite Trigonometric Functions

Use product-to-sum formulas to rewrite cosx.cosy

﻿12(cos⁡cos⁡(x−y))12(cos⁡cos⁡(2x−5y)+cos⁡cos⁡(2x−5y))\frac{1}{2}\left(\cos\cos\left(x-y\right)\right)\frac{1}{2}\left(\cos\cos\left(2x-5y\right)+\cos\cos\left(2x-5y\right)\right)21​(coscos(x−y))21​(coscos(2x−5y)+coscos(2x−5y))﻿

﻿12(cos⁡cos⁡(x−y)+cos⁡cos⁡(x+y))\frac{1}{2}\left(\cos\cos\left(x-y\right)+\cos\cos\left(x+y\right)\right)21​(coscos(x−y)+coscos(x+y))﻿

﻿12(cos⁡cos⁡(2x−5y)−cos⁡cos⁡(2x+5y))\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x+5y\right)\right)21​(coscos(2x−5y)−coscos(2x+5y))﻿

Use product-to-sum formulas to rewrite sin6x.sin4x

﻿12(sin⁡sin⁡5x+sin⁡sin⁡x)\frac{1}{2}\left(\sin\sin5x+\sin\sin x\right)21​(sinsin5x+sinsinx)﻿

﻿12(sin⁡sin⁡3x+sin⁡sin⁡x)\frac{1}{2}\left(\sin\sin3x+\sin\sin x\right)21​(sinsin3x+sinsinx)﻿

﻿12(cos⁡cos⁡(2x)−cos⁡cos⁡(10x))\frac{1}{2}\left(\cos\cos\left(2x\right)-\cos\cos\left(10x\right)\right)21​(coscos(2x)−coscos(10x))﻿

Use product-to-sum formulas to rewrite sin3x.sin2x

﻿12(sin⁡sin⁡5x+sin⁡sin⁡x)\frac{1}{2}\left(\sin\sin5x+\sin\sin x\right)21​(sinsin5x+sinsinx)﻿

﻿12(sin⁡sin⁡3x+sin⁡sin⁡x)\frac{1}{2}\left(\sin\sin3x+\sin\sin x\right)21​(sinsin3x+sinsinx)﻿

﻿12(cos⁡cos⁡(x)−cos⁡cos⁡(5x))\frac{1}{2}\left(\cos\cos\left(x\right)-\cos\cos\left(5x\right)\right)21​(coscos(x)−coscos(5x))﻿

Use product-to-sum formulas to rewrite sin2x.cosx

﻿12(sin⁡sin⁡5x+sin⁡sin⁡x)\frac{1}{2}\left(\sin\sin5x+\sin\sin x\right)21​(sinsin5x+sinsinx)﻿

﻿12(sin⁡sin⁡3x+sin⁡sin⁡x)\frac{1}{2}\left(\sin\sin3x+\sin\sin x\right)21​(sinsin3x+sinsinx)﻿

﻿12(cos⁡cos⁡(2x−5y)−cos⁡cos⁡(2x+5y))\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x+5y\right)\right)21​(coscos(2x−5y)−coscos(2x+5y))﻿

Use product-to-sum formulas to rewrite cosx.cos2x

﻿12(cos⁡cos⁡(2x−5y)−cos⁡cos⁡(2x−5y))\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x-5y\right)\right)21​(coscos(2x−5y)−coscos(2x−5y))﻿

﻿12(cos⁡cos⁡(x−y)−cos⁡cos⁡(x+y))\frac{1}{2}\left(\cos\cos\left(x-y\right)-\cos\cos\left(x+y\right)\right)21​(coscos(x−y)−coscos(x+y))﻿

﻿12(cos⁡cos⁡(−x)−cos⁡cos⁡(3x))\frac{1}{2}\left(\cos\cos\left(-x\right)-\cos\cos\left(3x\right)\right)21​(coscos(−x)−coscos(3x))﻿

Use product-to-sum formulas to rewrite sin7x.sin4x

﻿12(sin⁡sin⁡5x+sin⁡sin⁡x)\frac{1}{2}\left(\sin\sin5x+\sin\sin x\right)21​(sinsin5x+sinsinx)﻿

﻿12(cos⁡cos⁡3x−cos⁡cos⁡11x)\frac{1}{2}\left(\cos\cos3x-\cos\cos11x\right)21​(coscos3x−coscos11x)﻿

﻿12(cos⁡cos⁡2x−cos⁡cos⁡10x)\frac{1}{2}\left(\cos\cos2x-\cos\cos10x\right)21​(coscos2x−coscos10x)﻿

Use product-to-sum formulas to rewrite sin5x.sin2x

﻿12(cos⁡cos⁡(3x)−cos⁡cos⁡(7x))\frac{1}{2}\left(\cos\cos\left(3x\right)-\cos\cos\left(7x\right)\right)21​(coscos(3x)−coscos(7x))﻿

﻿12(sin⁡sin⁡3x+sin⁡sin⁡x)\frac{1}{2}\left(\sin\sin3x+\sin\sin x\right)21​(sinsin3x+sinsinx)﻿

﻿12(cos⁡cos⁡(x)−cos⁡cos⁡(5x))\frac{1}{2}\left(\cos\cos\left(x\right)-\cos\cos\left(5x\right)\right)21​(coscos(x)−coscos(5x))﻿

Use product-to-sum formulas to rewrite sin4x.cos2x

﻿12(sin⁡sin⁡6x+sin⁡sin⁡2x)\frac{1}{2}\left(\sin\sin6x+\sin\sin2x\right)21​(sinsin6x+sinsin2x)﻿

﻿12(sin⁡sin⁡3x+sin⁡sin⁡x)\frac{1}{2}\left(\sin\sin3x+\sin\sin x\right)21​(sinsin3x+sinsinx)﻿

﻿12(cos⁡cos⁡(2x−5y)−cos⁡cos⁡(2x+5y))\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x+5y\right)\right)21​(coscos(2x−5y)−coscos(2x+5y))﻿

Use product-to-sum formulas to rewrite sin3x.cos2x

﻿12(sin⁡sin⁡(5x)+sin⁡sin⁡(x))\frac{1}{2}\left(\sin\sin\left(5x\right)+\sin\sin\left(x\right)\right)21​(sinsin(5x)+sinsin(x))﻿

﻿12(sin⁡sin⁡(11x)+sin⁡sin⁡(x))\frac{1}{2}\left(\sin\sin\left(11x\right)+\sin\sin\left(x\right)\right)21​(sinsin(11x)+sinsin(x))﻿

﻿12(cos⁡cos⁡(2x−5y)−cos⁡cos⁡(2x+5y))\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x+5y\right)\right)21​(coscos(2x−5y)−coscos(2x+5y))﻿

Use product-to-sum formulas to rewrite sin6x.cos5x

﻿12(cos⁡cos⁡(2x−5y)−cos⁡cos⁡(2x−5y))\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x-5y\right)\right)21​(coscos(2x−5y)−coscos(2x−5y))﻿

﻿12(sin⁡sin⁡(11x)+sin⁡sin⁡(x))\frac{1}{2}\left(\sin\sin\left(11x\right)+\sin\sin\left(x\right)\right)21​(sinsin(11x)+sinsin(x))﻿

﻿12(cos⁡cos⁡(2x−5y)−cos⁡cos⁡(2x+5y))\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x+5y\right)\right)21​(coscos(2x−5y)−coscos(2x+5y))﻿

Incorrect

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$\frac{1}{2}\left(\cos\cos\left(x-y\right)\right)\frac{1}{2}\left(\cos\cos\left(2x-5y\right)+\cos\cos\left(2x-5y\right)\right)$

$\frac{1}{2}\left(\cos\cos\left(x-y\right)+\cos\cos\left(x+y\right)\right)$

$\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x+5y\right)\right)$

$\frac{1}{2}\left(\sin\sin5x+\sin\sin x\right)$

$\frac{1}{2}\left(\sin\sin3x+\sin\sin x\right)$

$\frac{1}{2}\left(\cos\cos\left(2x\right)-\cos\cos\left(10x\right)\right)$

$\frac{1}{2}\left(\sin\sin5x+\sin\sin x\right)$

$\frac{1}{2}\left(\sin\sin3x+\sin\sin x\right)$

$\frac{1}{2}\left(\cos\cos\left(x\right)-\cos\cos\left(5x\right)\right)$

$\frac{1}{2}\left(\sin\sin5x+\sin\sin x\right)$

$\frac{1}{2}\left(\sin\sin3x+\sin\sin x\right)$

$\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x+5y\right)\right)$

$\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x-5y\right)\right)$

$\frac{1}{2}\left(\cos\cos\left(x-y\right)-\cos\cos\left(x+y\right)\right)$

$\frac{1}{2}\left(\cos\cos\left(-x\right)-\cos\cos\left(3x\right)\right)$

$\frac{1}{2}\left(\sin\sin5x+\sin\sin x\right)$

$\frac{1}{2}\left(\cos\cos3x-\cos\cos11x\right)$

$\frac{1}{2}\left(\cos\cos2x-\cos\cos10x\right)$

$\frac{1}{2}\left(\cos\cos\left(3x\right)-\cos\cos\left(7x\right)\right)$

$\frac{1}{2}\left(\sin\sin3x+\sin\sin x\right)$

$\frac{1}{2}\left(\cos\cos\left(x\right)-\cos\cos\left(5x\right)\right)$

$\frac{1}{2}\left(\sin\sin6x+\sin\sin2x\right)$

$\frac{1}{2}\left(\sin\sin3x+\sin\sin x\right)$

$\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x+5y\right)\right)$

$\frac{1}{2}\left(\sin\sin\left(5x\right)+\sin\sin\left(x\right)\right)$

$\frac{1}{2}\left(\sin\sin\left(11x\right)+\sin\sin\left(x\right)\right)$

$\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x+5y\right)\right)$

$\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x-5y\right)\right)$

$\frac{1}{2}\left(\sin\sin\left(11x\right)+\sin\sin\left(x\right)\right)$

$\frac{1}{2}\left(\cos\cos\left(2x-5y\right)-\cos\cos\left(2x+5y\right)\right)$