Question 68

Solve the following.
$$\left(\frac{\sin 27^\circ}{\cos 63^\circ}\right) - \left(\frac{\cos 27^\circ}{\sin 63^\circ}\right)^{2}$$

Solution

$$\left(\frac{\sin 27^\circ}{\cos 63^\circ}\right) - \left(\frac{\cos 27^\circ}{\sin 63^\circ}\right)^{2}$$

$$\left(\frac{\sin(90^\circ - 63^\circ)}{\cos 63^\circ}\right) - \left(\frac{\cos(90^\circ - 63^\circ)}{\sin 63^\circ}\right)^{2}$$

= $$\left(\frac{\\cos 63^\circ}{\cos 63^\circ}\right) - \left(\frac{\sin 63^\circ}{\sin 63^\circ}\right)^{2}$$

= 1 - 1 = 0


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