Exams › SSC CGL (Prelims) › General

If \(\tan \theta = 1\), find the value of \((1+\sin \theta)(1-\cos \theta)\).

1. \(\frac{1}{2}\)
2. \(\frac{2-\sqrt{2}}{2}\)
3. \(\frac{1}{4}\)
4. \(\frac{1}{3}\)

Correct answer: \(\frac{1}{2}\)

Solution

If \(\tan \theta = 1\), then for the usual acute-angle case \(\theta = 45^\circ\). So \(\sin \theta = \cos \theta = \frac{1}{\sqrt{2}}\). Substituting gives \((1+\frac{1}{\sqrt{2}})(1-\frac{1}{\sqrt{2}})=1-\frac{1}{2}=\frac{1}{2}\).

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