Question

Evaluate the following :
$\sin {39}^{\circ }-\cos {51}^{\circ }$

Answer 1

Given trigonometric expression is $\sin {39}^{\circ }-\cos {51}^{\circ }$

We can write the expression as:

$\sin ({90}^{\circ }-{51}^{\circ })-\cos {51}^{\circ }$

We know that, $\sin ({90}^{\circ }-\theta )=\cos \theta$

$\Rightarrow \cos {51}^{\circ }-cos{51}^{\circ }=0$

Hence, $\sin {39}^{\circ }-\cos {51}^{\circ }=0$.