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If \sin\theta = \frac{3}{5} and\sin\phi = \frac{12}{13}, find \sin(\theta -\phi )

  • Option 1)

    \frac{23}{65}

  • Option 2)

    \frac{33}{65}

  • Option 3)

    -\frac{33}{65}

  • Option 4)

    -\frac{23}{65}

 

Answers (1)

best_answer

As we have learnt,

 

Subtraction Formulae -

\sin \left ( A-B \right )= \sin A\cos B-\cos A\sin B

- wherein

A and B are two angles.

 

 \sin(\theta - \phi) = \sin\theta\cos\phi - \cos\theta\sin\phi

                        = \frac{3}{5}\cdot \frac{5}{13} - \frac{4}{5}\cdot \frac{12}{13}

                        = \frac{15-48}{65} = -\frac{33}{65}

 


Option 1)

\frac{23}{65}

Option 2)

\frac{33}{65}

Option 3)

-\frac{33}{65}

Option 4)

-\frac{23}{65}

Posted by

Himanshu

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