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The value of \mathrm{ \frac{sin\left ( 90^{\circ}+\theta \right )sin\left ( 180^{\circ}+\theta \right )}{cos\left ( 90^{\circ}+\theta \right )}} is

 

Option: 1

\mathrm{cos\ \theta }

 


Option: 2

\mathrm{sin\ \theta}


Option: 3

\mathrm{tan\ \theta}

 


Option: 4

\mathrm{cot \theta}


Answers (1)

best_answer

Option (a) \mathrm{cos\ \theta}
The given expression is,

\mathrm{ \frac{sin\left ( 90^{\circ}+\theta \right )sin\left ( 180^{\circ}+\theta \right )}{cos\left ( 90^{\circ}+\theta \right )}}

Substituting the trigonometric formulas,

\mathrm{ \frac{sin\left ( 90^{\circ}+\theta \right )sin\left ( 180^{\circ}+\theta \right )}{cos\left ( 90^{\circ}+\theta \right )}=\frac{\left ( cos\ \theta \right )\left ( -sin\ \theta \right )}{\left ( -sin\ \theta \right )} }

\mathrm{\frac{sin\left ( 90^{\circ}+\theta \right )sin\left ( 180^{\circ}+\theta \right )}{cos\left ( 90^{\circ}+\theta \right )}=cos\ \theta }

Posted by

Deependra Verma

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