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2021-08-11

Express the product $\mathrm{sin}6x\times \mathrm{sin}4x$ as a sum or difference.

SchepperJ

Skilled2021-08-12Added 96 answers

Given:

To express the product$\mathrm{sin}6x\times \mathrm{sin}4x$ as sum or express it as difference.

Concept:

The study of side lengths and angles of triangle is studied by a relation called trigonometry.

The equation given is related to the expression below,

$\mathrm{sin}\left(6x\right)\times \mathrm{sin}\left(4x\right)=\frac{-1}{2}(-2\times \mathrm{sin}\left(6x\right)\times \mathrm{sin}\left(4\right))$

To obtain the relation derivate the right hand side by sin and cos rule,

$=\frac{-1}{2}(\mathrm{cos}(6x+4x)-\mathrm{cos}(6x-4x))$

The values of cos are sum and differenced to obtain the relation below,

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

Thus the product equation is expressed as sum or difference as below,

$\mathrm{sin}\left(6x\right)\times \mathrm{sin}\left(4x\right)=\frac{-1}{2}(\mathrm{cos}\left(10x\right)-\mathrm{cos}\left(2x\right))$

To express the product

Concept:

The study of side lengths and angles of triangle is studied by a relation called trigonometry.

The equation given is related to the expression below,

To obtain the relation derivate the right hand side by sin and cos rule,

The values of cos are sum and differenced to obtain the relation below,

Thus the product equation is expressed as sum or difference as below,

Jeffrey Jordon

Expert2021-12-10Added 2605 answers

Answer is given below (on video)

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