Mathematics

What is the value of the expression $$\dfrac{{\cos \left( {{{90}^0} + \theta } \right)\sec \left( { - \theta } \right)\tan \left( {{{180}^0} - \theta } \right)}}{{\sec \left( {{{360}^0} - \theta } \right)\sin \left( {{{180}^0} + \theta } \right)\cot \left( {{{90}^0} - \theta } \right)}} \ \ \ ? $$


ANSWER

$$-1$$


SOLUTION

$$\dfrac{{\cos \left( {{{90}^0} + \theta } \right)\sec \left( { - \theta } \right)\tan \left( {{{180}^0} - \theta } \right)}}{{\sec \left( {{{360}^0} - \theta } \right)\sin \left( {{{180}^0} + \theta } \right)\cot \left( {{{90}^0} - \theta } \right)}} \ \ \  $$

$$\dfrac{{\sin  { \theta } \sec  {  \theta } \left(-\tan  \theta  \right)}}{{\sec \theta (-\sin  \theta )(-\tan  \theta ) }}  $$

$$\implies -1$$

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Single Correct Medium Published on 17th 09, 2020
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