The value of \(\displaystyle\frac{\sin 30^\circ}{\cos^2 45^\circ}-\cot 45^\circ+\sin 90^\circ-7\cos 90^\circ\) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1
Each term is replaced by its standard value: \(\sin30^\circ=\frac{1}{2}\), \(\cos45^\circ=\frac{1}{\sqrt2}\), \(\cot45^\circ=1\), \(\sin90^\circ=1\), \(\cos90^\circ=0\).
First term: \(\displaystyle \frac{\sin30^\circ}{\cos^2 45^\circ}=\frac{1/2}{1/2}=1\)
Last term: \(7\cos90^\circ=7\times0=0\)
Value, with \(\cot45^\circ=1\) and \(\sin90^\circ=1\) in between: \(1-1+1-0=1\)