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The value of \cos (\alpha + \beta + \gamma ) + \cos (\gamma + \alpha - \beta ) + \cos (\alpha + \beta - \gamma ) + \cos (\beta + \gamma - \alpha ) is

  • Option 1)

    4\cos \alpha \cdot \cos \beta \cdot \cos \gamma

  • Option 2)

    2\cos \alpha \cdot \cos \beta \cdot \cos \gamma

  • Option 3)

    2\cos \alpha \cdot \cos \beta \cdot \cos \gamma

  • Option 4)

    4\sin \alpha \cdot \sin \beta \cdot \sin \gamma

 

Answers (1)

best_answer

As we learnt

 

Transformation Formulae -

 

transformation formulae 1

- wherein

These formula are also called C-D formulae.

 

 

 

Given expression can be rearranged as

                \cos (\alpha + \beta + \gamma ) + \cos (\alpha + \beta - \gamma ) + \cos (\gamma + \alpha - \beta ) + \cos (\beta + \gamma - \alpha )$

                = 2\cos \gamma \cdot \cos (\alpha + \beta ) + 2\cos \gamma \cos (\alpha - \beta )$

                = 2cosg(2cosa×cosb)

                = 4 cosa×cosb×cosg


Option 1)

4\cos \alpha \cdot \cos \beta \cdot \cos \gamma

Option 2)

2\cos \alpha \cdot \cos \beta \cdot \cos \gamma

Option 3)

2\cos \alpha \cdot \cos \beta \cdot \cos \gamma

Option 4)

4\sin \alpha \cdot \sin \beta \cdot \sin \gamma

Posted by

Himanshu

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