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# Find the value of $\dfrac{{\sin {{53}^ \circ }}}{{\cos {{37}^ \circ }}} + 2\tan {45^ \circ } - \dfrac{{\cos ec{{60}^ \circ }}}{{\sec {{30}^ \circ }}}$

Last updated date: 21st Jul 2024
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Hint:Consider the trigonometric functions to expand the equation with respect to its angles given. So that it will be cancelled easily and we will get the desired value.

To find the value of
$\dfrac{{\sin {{53}^ \circ }}}{{\cos {{37}^ \circ }}} + 2\tan {45^ \circ } - \dfrac{{\cos ec{{60}^ \circ }}}{{\sec {{30}^ \circ }}}$
We must know the Trigonometric function chart which helps us to find the values of the function very easily.
Let us write the given terms
$\dfrac{{\sin {{53}^ \circ }}}{{\cos {{37}^ \circ }}} + 2\tan {45^ \circ } - \dfrac{{\cos ec{{60}^ \circ }}}{{\sec {{30}^ \circ }}}$
As we cannot find the direct value of $\sin {53^ \circ }$, hence let us split the value into $\sin \left( {90 - 37} \right)$, we know that the value of tan45 then the equation becomes
$= \dfrac{{\sin \left( {90 - 37} \right)}}{{\cos 37}} + 2\left( 1 \right) - \dfrac{{\cos ec\left( {90 - 30} \right)}}{{\sec 30}}$
$= \dfrac{{\cos 37}}{{\cos 37}} + 2 - \dfrac{{\sec 30}}{{\sec 30}}$
$= 1 + 2 - 1$
$= 2$
Therefore, the value of
$\dfrac{{\sin {{53}^ \circ }}}{{\cos {{37}^ \circ }}} + 2\tan {45^ \circ } - \dfrac{{\cos ec{{60}^ \circ }}}{{\sec {{30}^ \circ }}} = 2$