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  • Pregunta: sinαsinβ+sinαsinβ tan(α−β)=sin(α−β)cos(α−β)=sinαcosβ+cosαsinβcosαcosβ−sinαsinβ=sinαsinβsinαcosβ+cosαsinβsinαsinβcosαcosβ−sinαsinβ =sinαsinβsinαcosβ+sinαsinβcosαsinβsinαsinβcosαcosβ−sinαsinβsinαsinβ=cotαcotβ+1cotβ−cotαsinαsinβ+sinαsinβ tan(α−β)=cos(α−β)sin(α−β)=cosαcosβ+sinαsinβsinαcosβ−cosαsinβ=cosαcosβcosαcosβ+sinαsinβcosαcosβsinαcosβ−cosαsinβ

    student submitted image, transcription available below

    student submitted image, transcription available below

    student submitted image, transcription available below

    Muestra el texto de la transcripción de la imagen
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    Queda solo un paso para resolver este problema.
    Solución
    Paso 1

    Given identity is

    tan⁡(α−β)=cot⁡β−cot⁡αcot⁡αcot⁡β+1

    Now, L.H.S= tan⁡(α−β)

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Texto de la transcripción de la imagen:
sinαsinβ​+sinαsinβ​ tan(α−β)=sin(α−β)cos(α−β)​=sinαcosβ+cosαsinβcosαcosβ−sinαsinβ​=sinαsinβsinαcosβ+cosαsinβ​sinαsinβcosαcosβ−sinαsinβ​​ =sinαsinβsinαcosβ​+sinαsinβcosαsinβ​sinαsinβcosαcosβ​−sinαsinβsinαsinβ​​=cotαcotβ+1cotβ−cotα​ sinαsinβ​+sinαsinβ​ tan(α−β)=cos(α−β)sin(α−β)​=cosαcosβ+sinαsinβsinαcosβ−cosαsinβ​=cosαcosβcosαcosβ+sinαsinβ​cosαcosβsinαcosβ−cosαsinβ​​ =cosαcosβcosαcosβ​+cosαcosβsinαsinβ​cosαcosβsinαcosβ​−cosαcosβcosαsinβ​​=cotαcotβ+1cotβ−cotα​ Establish the identity. tan(α−β)=cotαcotβ+1cotβ−cotα​ Choose the sequence of steps below that verifies the identity. A. tan(α−β)==​cos(α−β)sin(α−β)​=cosαcosβ+sinαsinβsinαcosβ−cosαsinβ​=sinαsinβcosαcosβ+sinαsinβ​sinαsinβsinαcosβ−cosαsinβ​​sinαsinβcosαcosβ​+sinαsinβsinαsinβ​sinαsinβsinαcosβ​−sinαsinβcosαsinβ​​=cotαcotβ+1cotβ−cotα​​