What is the value of \(\left(\displaystyle\frac{\sin 27^\circ}{\cos 63^\circ}\right)^2+\left(\displaystyle\frac{\cos 63^\circ}{\sin 27^\circ}\right)^2\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2
Since \(27^\circ+63^\circ=90^\circ\), the two angles are complementary and \(\cos 63^\circ=\cos(90^\circ-27^\circ)=\sin 27^\circ\). Each fraction is therefore 1.
\(\displaystyle\frac{\sin 27^\circ}{\cos 63^\circ}=1\) and \(\displaystyle\frac{\cos 63^\circ}{\sin 27^\circ}=1\)
Value \(=1^2+1^2=2\)